When you want to design and simulate a real issue (be a question of population dynamism in ecology, tumor growth in biomedical engineering, combustion dynamics in new-generation rocket engines - for example at SpaceX, prediction of solar storms and magnetic reconnection phenomena in solar physics, simulation of turbulence and turbulent combustion in fluid mechanics) the engineer or the researcher in applied mathematics or in "computational science" has to use a range of digital methods and must be able to analyze it mathematically, assess in terms of quality and computational efficacity, and finally, implement.

This course offers an introduction to numerical analysis, starting with the mathematical foundations on which numerical methods are based through to the implementation and the use of these methods on Jupyter notebooks (an active field at the Ecole Polytechnique), including their stability in relation to mathematical conditioning of the problems posed. The link is made with applications to understand the extent to which this type of method can be used from a practical point of view. Implementations of these methods in existing digital libraries are also documented.

Every class sessions include an analysis of the mathematical foundations on which a numerical method class is built, a description and analysis of the digital method (with a historical perspective). Those two aspects are covered during the course. The PC offers a review and an in-depth look at some concepts of the course, use of the method in the context of Jupyter notebooks and a description of how students can implement the method in a notebook to be handed in for the next class session.

Machine learning is a scientific discipline that is concerned with the design and development of algorithms that allow computers to learn from data. A major focus of machine learning is to automatically learn complex patterns and to make intelligent decisions based on them.

This course focuses on the methodology underlying supervised and unsupervised learning, with a particular emphasis on the mathematical formulation of algorithms, and the way they can be implemented and used in practice. We will therefore describe some necessary tools from optimization theory, and explain how to use them for machine learning.

Proofs will not be made during the lectures: some will be made during the labs others could be found in a document. Finally, each lab will finish with a numerical lab in Python

Validation

• A Kaggle challenge (10 points)
• A final exam (10 points)

This a Data Camp based on the challenges proposed by the ENS: https://challengedata.ens.fr/

You can choose any of the proposed challenges. You will have to work in groups in groups of three to four students and have to provide a solution by the end of march. To help you, we will organize non mandatory coaching sessions.

Responsables de l'option:

Stéphane Gaubert
gaubert@cmapx.polytechnique.fr

Frédéric Meunier
frederic.meunier@enpc.fr 

mail générique : map593@meslistes.polytechnique.fr

Coordinatrice des enseignement du Département de Mathématiques Appliquées 
Tél: 01 69 33 46 07
Fax: 01 69 33 46 46.
mail : nathalie.rodrigues@polytechnique.edu

Cette option regroupe deux disciplines complémentaires : l'automatique, art de la commande de systèmes dynamiques, et la recherche opérationnelle, qui met en œuvre les techniques d'optimisation continue et discrète.
Ces deux secteurs connaissent une demande soutenue. L'automatique est très utilisée depuis longtemps en aéronautique et dans les processus de production (chimie, cimenteries, laminage, biotechnologies). Avec l'invasion de l’électronique elle devient un élément-clé dans de nouveaux secteurs comme l'automobile. Elle intervient aussi dans la commande de grands systèmes. Elle comprend des sujets d’interface avec plusieurs domaines, comme l’ingéniérie quantique ou l’écologie. La recherche opérationnelle est la technique fondamentale de résolution des problèmes de gestion complexes : plans de production, horaires de transport, affectation de moyens, conception de réseaux, investissements. Ces deux disciplines sont présentes dans les grandes entreprises mais aussi dans de petites sociétés. Elles occupent une place importante dans les universités françaises comme étrangères.

L'option "Automatique et Recherche Opérationnelle" est conçue pour des élèves qui cherchent une formation dans cette spécialité, soit pour aborder un problème industriel, soit pour s'initier à la recherche et ce, quel que soit le choix ultérieur de leur carrière. Pour les élèves très motivés qui veulent s'expatrier durant leur stage d'option, il est possible de trouver des sujets de stages dans des universités ou des petites sociétés étrangères.

Exemples de stages effectués les années passées :

Automatique :

• Stabilisation de satellites d’astéroïdes
• Commande optimale dans le domaine spatial
• Planification de trajectoires de robots

Recherche opérationnelle :

• Optimisation de réseaux telecom
• Gestion de voies ferrées
• Optimisation de production électrique
• Gestion de réserves de gaz
• Jeux de congestion appliqués au traffic routier.
• Optimisation semi-algébrique

Organismes d'accueil proposant des stages :

• Laboratoires publics de recherche : IFREMER, IFP, INRIA, ONERA, LAAS, Ecoles d'ingénieurs (dont ENPC) et Universités ( dont UPMC).
• Grandes entreprises et centres de recherche appliquée : Air Liquide, Air France, Innovation 24 (Bouygues), Orange Labs, EDF, Engie, Amadeus, SNCF.
• Organismes d'accueil à l'étranger : Universités étrangères (Columbia, San Diego,Berkeley, Cornell Melbourne, TU-Berlin) ou européennes, IBM Singapore.

Professors in charge of the option:

Stéphane Gaubert
gaubert@cmapx.polytechnique.fr

Frédéric Meunier

frederic.meunier@epnc.fr 

map593@meslistes.polytechnique.fr

Secretariat of the Applied Mathematics Department:
Tel: 01 69 33 46 07
Nathalie Rodrigues
nathalie.rodrigues@polytechnique.edu

This option brings together two complementary disciplines: automatic, the art of controlling dynamic systems, and operational research, executing continuous and discrete optimization techniques. Thes sectors experience a sustained demand.
Automatic is very used in aeronautics and in production processes (chemistry, cement, lamination, biotechnologies). With the electronical invasion, it becomes a key element in the new sectors such as automobile, it also intervenes in the control of large system. It includes interface with several fields, such as quantum engineering or ecology. Operational research is the fundamental problem-solving technique for complex management: production plans, transport schedule, ressource allocations, network design, investments. These two disciplines are present in large and small companies, and they play an important role in French and foreign universities.

The "Automation and Operational Research" option is designed for students searching a training in this speciality, either to address an industrial issue, or to initiate research, regardless of their future career choices. For the motivated student who want to go abroad during their research internship, it is possible to find subjects of internships in foreign universities or small societies.

Example of internships of the earlier years:

Automatic:

• Stabilization of asteroidal satellites
• in the spatial sector
• Planning of robot trajectories

Operational research:

• Optimization of the telecom network
• Railroad management
• Optimization of electricity production
• Management of gas reserve
• Congestion games applied to road traffic
• Semi-algebraic optimization

Host organizations offering internships:

• Public research laboratories: IFREMER, IFP, INRIA, ONERA, LAAS, Engineering schools (including ENPC) and Universités (including UPMC).
• Large companies and applied centers of research: Air Liquide, Air France, Innovation 24 (Bouygues), Orange Labs, EDF, Engie, Amadeus, SNCF.
• Foreign host organizations: Foreign universities () or European, IBM Singapore.

Responsables d'option :
Eduardo Abi-Jaber
Mail : map595@meslistes.polytechnique.fr

Charles-Albert Lehalle
Mail : map595@meslistes.polytechnique.fr

Huyên Pham
Mail : map595@meslistes.polytechnique.fr

Coordinatrice des Enseignement du Département de Mathématiques Appliquées 
Nathalie Rodrigues
T. +33 (0)169334607 – nathalie.rodrigues@polytechnique.edu

Les stages proposés en Mathématiques financières se passent en général dans les centres de recherche des salles de marché des banques ou d’autres organismes, tels des fonds d'investissement. Pour certains stages, il est indispensable d’avoir suivi le cours "Modèles stochastiques en finance" de troisième année. Les stages à l’étranger se déroulent soit dans la banque, soit dans des centres de recherche académiques.

Certains stages nécessitent plusieurs entretiens avec différentes équipes.

Exemples de stages proposés les années précédentes :

En France

• AXA
  Optimisation de stratégie tarifaire

• CMAP
  Principal-Agent à plusieurs agents et à une dynamique de sauts. Applications à la structuration et la tarification des contrats d'électricité

• CREDIT SUISSE
  Méthodes génétiques pour l'optimisation de portefeuilles

• KEPLER CHEVREUX
  Dynamiques de données de carnet d'ordres et détection d'algorithmes

• SOCIETE GENERALE
  Pricing de produits structurés très long terme

• UNIVERSITE PARIS 7
  Modèles financiers avec arbitrage, application à la gestion actif-passif long terme

A l'étranger

• BLOOMBERG LP
  Calibration of a Path Dependent Volatility model to the VIX and S&P markets*

• BNP PARIBAS London Branch
  Models for Overnight indexed swap rates and Libor dynamics, and related Market risk

• BRITISH PETROLEUM
  Application de techniques de Machine Learning à la méthode de Monte-Carlo des moindres carrés

• DEUTSCHE BANK Londres
  Pricing and risk management of interest rate derivatives
  
  
• GOLDMAN SACHS
  Predictive flow Analytics & inventory optimization
  
  
• IMC Trading
  Identification of the impact of market participants on the European Futures Market
  
  
• JANE STREET
  The volume synchronized probability of informed trading
  
  
• JP MORGAN
  Capital optimization, funding optimization, derivates clearing businesses, credit value adjustement
  
  
• JUMP TRADING INTERNATIONAL
  Latent order book in the context of market impact and liquidity drought
  
  
• MONASH UNIVERSITY
  Option pricing with linear market impact
  
  
• SQUAREPOINT CAPITAL
  Multi-period portfolio optimization to manage tail risk in equities
  
  
• UNIVERSITY OF OXFORD
  Numerics for the robust pricing and hedging problem in discrete time

Professors in charge of the option:

Eduardo Abi-Jaber
Mail : map595@meslistes.polytechnique.fr

Charles-Albert Lehalle
Mail : map595@meslistes.polytechnique.fr

Huyên Pham
Mail : map595@meslistes.polytechnique.fr

Teaching coordinator of the Applied Mathematics Department
Nathalie Rodrigues
T. +33 (0)169334607 – nathalie.rodrigues@polytechnique.edu

Internships offered in Financial mathematics generally take place in centers of research of banks or other organisms, such as investment funds. For some internships, it is mandatory to have taken the Year-3 course of "Stochastic models in finance". Internships abroad take place either in the bank or in academical centers of research.

Some internships require several interviews with different teams.

Example of internships of the earlier years:

En France

• AXA
  Optimization of pricing strategy
  
  

• CMAP
  Principal-Agent to several agents and to a jump dynamic. Applications to the structuing and pricing of electricity contracts
  
  
  CREDIT SUISSE
  Genetical methods for portfolio optimization
  
  

• KEPLER CHEVREUX
  Dynamics of order-book data and algorithm detection
  
  

• SOCIETE GENERALE
  Pricing de produits structurés très long terme
  
  

• UNIVERSITE PARIS 7
  Financial models with arbitraging, application to long-term asset and liability management

Abroad

• BLOOMBERG LP
  Calibration of a Path Dependent Volatility model to the VIX and S&P markets
  
  

• BNP PARIBAS London Branch
  Models for Overnight indexed swap rates and Libor dynamics, and related Market risk
  
  

• BRITISH PETROLEUM
  Application de techniques de Machine Learning à la méthode de Monte-Carlo des moindres carrés
  
  

• DEUTSCHE BANK Londres
  Pricing and risk management of interest rate derivatives
  
  

• GOLDMAN SACHS
  Predictive flow Analytics & inventory optimization
  
  

• IMC Trading
  Identification of the impact of market participants on the European Futures Market
  
  

• JANE STREET
  The volume synchronized probability of informed trading
  
  

• JP MORGAN
  Capital optimization, funding optimization, derivates clearing businesses, credit value adjustement
  
  

• JUMP TRADING INTERNATIONAL
  Latent order book in the context of market impact and liquidity drought
  
  

• MONASH UNIVERSITY
  Option pricing with linear market impact
  
  

• SQUAREPOINT CAPITAL
  Multi-period portfolio optimization to manage tail risk in equities
  
  

• UNIVERSITY OF OXFORD
  Numerics for the robust pricing and hedging problem in discrete time

Teaching supervisor: Arnaud Echard

This course lets you discover a core scientific discipline, biology, and prepares you for several other 2nd year biology courses, as well as for more advanced, 3rd year programs offered by the Biology department of Biology. This is a basic biology course, designed for students from all scientific origins.

It will reveal the logic of the living world and will show how biology, an expanding scientific discipline, is developing more and more at the interface with physics, chemistry, informatics, mathematics and engineering sciences.

The course will show the distinctive features and the informative molecules (DNA, RNA and proteins) shared by all living organisms. The main regulations controlling RNA and protein production will be detailed. This will enable us to understand how cells regulate their gene expression to answer their needs and adapt to environmental changes. It presents, in a progressive and sometimes deliberately simplified way, the major advances in the biological sciences of the 20th and 21st centuries. The course also provides an understanding of the major contemporary societal issues linked to the life sciences.

Course Language : French.

Experimentation is central to progress in biology. It enables working hypotheses to be tested. Thanks to cycles of hypothesis verification and refinement, we end up with predictive models, despite the great complexity of the objects studied: living beings.

We cannot guarantee that a student will be registered for a specific theme. The distribution of students is based on supply and demand. The following themes are likely to be opened:

- Bioluminescence:

The chemical energy extracted from organic molecules by living beings can be transformed into thermal energy, mechanical energy, electrical energy, and even light energy. This last property is more widespread than we think since it exists in several hundred species as diverse as bacteria, fungi and animals. We will study the green fluorescent protein (GFP) of the jellyfish Aequorea victoria. We will use the tools of genetic engineering, biochemistry and biophysics to understand the origin of this fluorescence and how to exploit it in various biotechnological fields. Firefly tail luciferin will also be discussed to understand the origin and mechanism of its bioluminescence.

-Antibodies: from immune defense to clinical diagnosis:

Antibodies, central molecules in the humoral immune response, play an essential role in the prevention of infections. Moreover, thanks to their precise characterization, they have also become essential tools for research, medical diagnosis and therapy, in particular anti-cancer. This Modal aims to characterize the biochemical properties of antibodies as well as to illustrate several examples of the use of antibodies in research and medical diagnosis. The use of a large number of classical techniques of biochemistry and biology also make this Modal an excellent introduction to laboratory work.

- Intracellular imaging:

The organization and dynamics of the cytoskeleton play an essential role in many eukaryotic cell life processes, such as migration, division or intracellular transport. The objective of this Modal is to observe the different components of the cytoskeleton (microtubule and actin filaments) inside human cells. It is an opportunity to introduce multiple techniques in cell biology (culture of human cells, immunocytochemistry, transfection), microscopy and digital modeling.

- Cloning:

This modal allows you to discover the key tools and techniques used daily in laboratories. Baker's yeast dihydrofolate reductase (DHFR) is an essential protein conserved in all eukaryotes. Thanks to its key role in cell growth and metabolism, DHFR is of pharmacological interest. It is the target of the few drugs that are used for the treatment of a wide spectrum of diseases. We will clone the gene coding for the eukaryotic DHFR in a bacterium, we will induce its expression and we will purify the protein produced. Finally, an enzymatic test will make it possible to functionally characterize the purified protein.

-Synthetic biology: design and construction of synthetic genetic oscillators:

Synthetic biology aims to design and build artificial life forms that perform a given function. Gene regulatory networks are sets of genes that interact with each other and with other molecules, via their expression products, allowing mutual control of their expression levels. One possible approach to synthetic biology is to modify existing genetic networks or design new ones, opening the way to the design of new biological functions. This is a very active area of ​​research with many potential applications. The purpose of this Modal is the study and fabrication of synthetic genetic oscillators, that is to say networks of unnatural genes with an oscillating behavior. It uses the following methods and techniques: modeling of gene networks, genetic engineering, cell culture, fluorescence microscopy, image analysis.

Optional Year 3 project for both periods.

Alone or in pairs projects will be the subject of discussions between students and teachers and will be assiociate to one of the followed units.

The proposed projects by the Biology Department will be available in the BioInformatics PA.

The project ca be carried out according to one of the three following options with the teachers during the starting PA lecture hall: P1 or P1 and P2

- BIO511

Research project: the first option involves a research activity in laboratory. In most projects of this option, a part of data production will be followed by an analysis and modeling part.

It is a first introduction and a personal initial contact with the research world.

- Bibliographic project: This option involves developing a bibliographic in-depth research on a specific subject related with one of the year 3 course.

The purpose is to be capable of presenting this topics in a concise, understandable and instructive way in the form of a course presentation with a written document.

- Project development: This option involves developing a funding request for a research project. The purpose will be to define a scientific project innovative and ambitious on one of the topics proposed in year 3, to write and present it orally.

For all this options, exchanges between teachers in the department and between departments are highly encouraged. All these topics can also be developed in engineering perspective, incuding the developement of methods, tools, software, databases and genetically modified organisms.

The purpose of the year 3 project is to start a personal project on a biology research topic by combining reflection, bibliographic analysis and/or experiments and data analases. The project is to be realized alone or in pairs (possibly more but a clear division of tasks will be required). It will be attached to one of the year 3 teachers that you have chosen so you can discuss your progress and interogations regurarly with your teachers. In order that your projects are succesful, a real engagement is required, both in terms of working time you will devote to it in the first weeks and in terms of openness and maturity you must demonstrate, to collect sources of information from your teachers but also from teachers in other departments or regional researchers. You will learn the most by keeping the project alive.

Schedule:

A list of projects and subjects will be presented at the lecture hall 0 in September.

At the end of the day, each student must have defined a project, a subject and/or chosen a referent teacher. The projects and subjects presented remain open and are intended to give you a starting point and to show you the different fields of expertise of the biology department's teachers. Feel free to develop these projects or to discuss with the teachers to bring out new ones that are important to you, our only goal is to make sure that these projects are coherent and realizable, so you can develop your full potential. You can also choose an article analysis with a unit of P1, especially BIO571.

Evaluation modality:

• September to end of February: project development, a half-day each week with your tutor.
• Mid-December: intermediate defense organized at the end of the first period.
• Mid-March/end of March: redaction of a short report and oral defense.

A 10 minutes oral presentation (15 minutes for a duo) will be followed by a 15 minutes discussion with coordinators and project tutors. We do not ask for a written report but we encourage you to deliver a report to your renferent so they can keep a record of your work. Check with them for the expected form.

Course language: French

Biodiversity loss, climate change and the alteration of ecosystem functioning represent major challenges for society and policy makers. The aim of this course is to provide the theoretical and methodological basics essential to understand the causes and consequences of the challenges imposed by global change. The concepts and examples presented during the course will illustrate the complex relationships between biodiversity, ecological processes and human societies, and the need to adopt an interdisciplinary approach (mathematical modelling of a population, physico-chemical properties of soils and vegetation dynamics, human health and air quality, etc.) to address current environmental challenges.

Bio_52991_EP (BIO591) - Biology and Ecology

The Research internship opens fundamental, biomedical, or applied research laboratories (pharmaceutical industry, biotechnology) to students tempted by an in-depth study in Life Sciences, whether in microbiology, virology, immunology, neurobiology, embryology , in structural biology, in molecular biology, in cellular biology, in bioinformatics, in ecology...

Internship topics from previous years are available in a secure sharing space on the Ecole Polytechnique website:
-Subjects of research internships from previous years: (history of X04 to X12) 
https://gargantua.polytechnique.fr/siatel-web/app/auth/login?auth=1/
Folders My documents/Reports/General content Reports/SOI/X2004.....X2012

The student will be able, with the advice of the coordinator and the teaching team, to draw the thematic outlines of their internship, then actively participate, thanks to laboratory visits, in the ultimate definition of their Research internship subject.
The scientific research internship in Biology consists of a minimum of 16 weeks of work in the laboratory. This internship can take place in an academic laboratory or in a company laboratory. Internships take place in the Province, in Paris or in the Paris region (CNRS, INSERM, Institut Pasteur, Institut Curie, INRA, CEA, Universities, etc.) and abroad (United States, Germany, Canada, Italy, Spain, Japan, Portugal etc...)

Final Report: 
We will need an electronic version (in PDF format only) of your microthesis (twenty pages maximum all inclusive) to send by email. 
Reports can be delivered in French or English, as you prefer. 
You will ensure that these documents reach Catherine MORAIS catherine.morais@polytechnique.edu, the members of the jury, the referring teacher of your internship IMPERATIVELY five days minimum excluding weekends before your defense.
This poses no problem if one or other of the documents sent to X is written in English (final report and evaluation sheet sent by your internship director). 
Apart from the limit of 20 pages, annexes included, we have no particular requirements. This is a classic scientific report, and your host laboratory will provide you with useful advice on this subject. In short, the report must introduce first and last name, promotion, the subject by placing it in its context, cover page of the report written according to the model attached in the appendix. A MANDATORY summary in French and English of half a page maximum, all on the same page, then develop the results obtained, and finally discuss them.

Bibliographic references must also be indicated according to current standards for research articles.
The materials and methods used must also be described.
We remind you that compliance with deadlines will be taken into account in the rating. 
NO PAPER VERSION REQUESTED

- Defense: The oral defense must be carried out in person at the École Polytechnique (defense in French or English). 
The organization of the defense is managed by the department (duration, jury, public, etc.) is managed by the department.

- Internship director invitation: 
Your internship director will be invited to participate in the defense. However, his presence at the defense is not obligatory.  Your internship director must IMPERATIVELY send us his/her assessment of the work carried out and the way in which it was carried out, by completing the evaluation form sent by the Department.  This assessment must be sent IMPERATIVELY three days before the defense, by e-mail to: Catherine MORAIS catherine.morais@polytechnique.edu, to the members of the jury, to the teacher responsible for your internship.

----------------- 
Joint internships:
For students entering a double degree engineering course in the fourth year, the subject, the location of the internship, the terms of the intermediate follow-up and the defense jury are, in certain cases, defined jointly by those responsible for the internship. research of l’X and by teachers of additional diploma training.

Joint internships allow the student to implement, in a real setting, an experimental or theoretical scientific approach, while discovering one of the sectors covered by the additional training.

- Coordinator - Responsible:
Yves MECHULAM - Tel: 4885 - yves.mechulam@polytechnique.edu
- Department assistant:
Catherine Morais - Tel: 4025 - catherine.morais@polytechnique.edu

- Teachers: all members of the department

Course language: French

ECTS credits: 20

BIO_54468_EP - Exploration et analyse statistique d'ensembles de données complexes

Descriptif du cours :

L’analyse d’échantillons environnementaux a connu une transformation remarquable grâce aux progrès récents de l’écologie moléculaire et de la chimie analytique. Les méthodologies à haut débit utilisées dans ces domaines ont permis aux chercheurs de générer de vastes volumes de données, offrant ainsi un aperçu sans précédent des complexités environnementales. Cependant, ces données prennent souvent la forme d’ensembles de données de grande dimension. Résumer et extraire des informations précieuses à partir de ces ensembles de données complexes et multidimensionnels est un défi et nécessite des méthodes spécifiques. 

BIO_54468_EP présente une gamme de méthodes et de concepts théoriques, des statistiques descriptives aux statistiques multivariées, un ensemble de méthodes puissantes pour analyser et interpréter des données impliquant plusieurs variables simultanément. Avec une combinaison équilibrée de théorie et de travaux pratiques, les étudiants apprendront à appliquer diverses méthodes statistiques à des problèmes du monde réel, leur permettant de tirer des informations significatives à partir d'ensembles de données complexes. Le cours vise à fournir aux étudiants une solide compréhension des principes des statistiques descriptives et des méthodes multivariées ainsi que les compétences nécessaires pour sélectionner et utiliser efficacement ces méthodes dans leur propre travail.

Examen :
L'évaluation du cours comprend deux éléments principaux :

   1. Examen écrit : Un examen de 3 heures à livre fermé, sans accès aux documents, notes ou calculatrices.
   2. Projet personnel : Chaque étudiant devra réaliser un projet personnel, qui sera évalué séparément.

Teaching supervisor: Arnaud Echard

This course lets you discover a core discipline and prepares you for several other 2nd year biology courses, as well as for more advanced, 3rd year programs offered.

It will reveal the logic of the living world and will show how biology, an expanding scientific discipline, is developing more and more at the interface with physics, chemistry, informatics, mathematics and engineering sciences.

The course will show the distinctive features and the informative molecules (DNA, RNA and proteins) shared by human beings. The main regulations controlling RNA and protein production will be detailed. This will enable us to understand how cells regulate their gene expression to answer their needs and adapt to environmental changes.

Course Language : French.

Experimentation is central to progress in biology. It enables working hypotheses to be tested. Thanks to cycles of hypothesis verification and refinement, we end up with predictive models, despite the great complexity of the objects studied: living beings.

We cannot guarantee that a student will be registered for a specific theme. The distribution of students is based on supply and demand. The following themes are likely to be opened:

- Bioluminescence:

The chemical energy extracted from organic molecules by living beings can be transformed into thermal energy, mechanical energy, electrical energy, and even light energy. This last property is more widespread than we think since it exists in several hundred species as diverse as bacteria, fungi and animals. We will study the green fluorescent protein (GFP) of the jellyfish Aequorea victoria. We will use the tools of genetic engineering, biochemistry and biophysics to understand the origin of this fluorescence and how to exploit it in various biotechnological fields. Firefly tail luciferin will also be discussed to understand the origin and mechanism of its bioluminescence.

-Antibodies: from immune defense to clinical diagnosis:

Antibodies, central molecules in the humoral immune response, play an essential role in the prevention of infections. Moreover, thanks to their precise characterization, they have also become essential tools for research, medical diagnosis and therapy, in particular anti-cancer. This Modal aims to characterize the biochemical properties of antibodies as well as to illustrate several examples of the use of antibodies in research and medical diagnosis. The use of a large number of classical techniques of biochemistry and biology also make this Modal an excellent introduction to laboratory work.

- Intracellular imaging:

The organization and dynamics of the cytoskeleton play an essential role in many eukaryotic cell life processes, such as migration, division or intracellular transport. The objective of this Modal is to observe the different components of the cytoskeleton (microtubule and actin filaments) inside human cells. It is an opportunity to introduce multiple techniques in cell biology (culture of human cells, immunocytochemistry, transfection), microscopy and digital modeling.

- Cloning:

This modal allows you to discover the key tools and techniques used daily in laboratories. Baker's yeast dihydrofolate reductase (DHFR) is an essential protein conserved in all eukaryotes. Thanks to its key role in cell growth and metabolism, DHFR is of pharmacological interest. It is the target of the few drugs that are used for the treatment of a wide spectrum of diseases. We will clone the gene coding for the eukaryotic DHFR in a bacterium, we will induce its expression and we will purify the protein produced. Finally, an enzymatic test will make it possible to functionally characterize the purified protein.

-Synthetic biology: design and construction of synthetic genetic oscillators:

Synthetic biology aims to design and build artificial life forms that perform a given function. Gene regulatory networks are sets of genes that interact with each other and with other molecules, via their expression products, allowing mutual control of their expression levels. One possible approach to synthetic biology is to modify existing genetic networks or design new ones, opening the way to the design of new biological functions. This is a very active area of ​​research with many potential applications. The purpose of this Modal is the study and fabrication of synthetic genetic oscillators, that is to say networks of unnatural genes with an oscillating behavior. It uses the following methods and techniques: modeling of gene networks, genetic engineering, cell culture, fluorescence microscopy, image analysis.

Biotechnology for Health and Agriculture (S. Thomine et A. Meunier)

I) Biotechnology & Medicine: Towards Regenerative Therapies (A. Meunier)
How to repair tissue damaged by age or disease? In addition to chemotherapy, organ transplants and prostheses have attempted to respond to this challenge by replacing the damaged organ or tissue. When possible and tolerated by the body, these very heavy interventions require lifelong treatments. Advances in cellular and molecular biology have led to the emergence of new therapies, using evolutionarily selected biological processes to repair deficient tissues. This part of medicine, called "regenerative medicine", targets a definitive cure of the patient and is the subject of a very active research. A large part of the course will be devoted to stem cell biology, a field in full expansion and whose influence and applications are growing. We will see that some human cells have kept a stem cell potential. In addition, we are now able to reprogram differentiated adult cells into pluripotent stem cells (iPS). We will also show how the use of parasites specialized in the diversion of cellular machinery, combined to the use of bacterial enzymatic systems such as the CRISPR / Cas9 system allow the modification of gene expression in targeted cell types. Finally, we will discuss the ethical issues as well as the limits to be imposed on the modification and the commercialization of living.

II) Biotechnology & agriculture (S. Thomine)
With increasing world population and limited resources availability (e.g. arable land, fossil carbon, and water), food security remains a major challenge. This challenge is amplified by an increasing use of plant biomass for green chemistry and energy production. At the same time, climate change and the importance of preserving the environment and biodiversity cause additional constraints on production systems. In this context, it seems necessary to develop a "sustainable intensification" of agriculture.
In this course, we will see how plant biology and biotechnology can contribute to tackle these challenges, and their potential risks or limitations. In the first part we will discuss the genetic, molecular and cellular bases of plant development and reproduction and their domestication. In a second part, we will present recent developments in genomics and biotechnologies (cloning, transgenesis and genome editing) and will see how they can contribute to plan breeding to meet the different agronomic, industrial, environmental or social challenges.

Required level: At least one biology module in year 2.
Course language: English

Epigenetics and non-coding RNAs

In complex organisms, the study of the processes that allow genetic information carried by DNA to be stored and decoded in time and space, in a context consisting for the most part of DNA that does not carry protein information (98% of the mammalian genome is non-coding), constitutes a new field of research with major issues in both basic science and applied research.

While we thought we had already gone very deep into the decoding of genetic material, thanks to the advancement of DNA and RNA sequencing technologies, we are once again facing new scientific, technological and ethical challenges to approach new codes related to epigenetic characteristics and non-coding RNAs, which will allow us to better understand the functioning of living organisms as well as the deregulation of genome expression in pathologies.

Indeed, these advances have made us realize that the simple decoding of the sequences of our genome would not be enough to understand (i) the differential behavior of the different tissues of the organisms, (ii) the cell adaptation to endogenous/exogenous stress, but also (iii) the pathologies associated with DNA damage (mutations). As such, epigenetics, a relatively recent scientific discipline that goes beyond genetics, consists of studying the way by which DNA is decoded in a stable and reversible way, considering not only the genomic sequences, but also additional codes consisting of chemical modifications of DNA and associated factors. Non-coding RNAs also play major roles in genome regulation, whether or not linked to epigenetics. Surprisingly, the "epigenetic" codes, which are not written in the sequence of the 4 bases present in the genomes, can be transmitted from one generation to another in certain living organisms and could pass an environmental footprint to the offspring.

Issues:
• How is genetic information decoded in different ways, beyond the DNA sequence, to give different phenotypes in different cells or different organisms (e.g., twins) with the same genotype? Concept of cellular identity.
• What is the contribution of non-coding RNAs to these processes?
• What is the impact of the environment on gene expression in the short, medium and long term? Notion of cellular memory.
• What is the implication of non-coding RNAs and epigenetic marks in pathologies as well as in the diagnostic and therapeutic potential?

Required level: Attended at least one biology module in year 2
Course language: English
ECTS credits: 4

The state of scientific knowledge shows that responses to climate change, biodiversity collapse, resources limits and pollutions require major transformations in all systems: energy, industry, agriculture and food, land use, transportation, infrastructure, and cities, at an unprecedented scale and speed.

The course aims to develop a systemic, historical and forward-looking understanding of complex natural and human systems dynamics and their interactions at play in sustainability issues and solutions. The course will consolidate a rigorous scientific culture and provide tools for analyzing and addressing the major issues of sustainable development in their environmental, economic, and social dimensions. It will lay the groundwork for developing mastery of analytical methods and skills to become engineers who are actors in the transformations that the current crisis calls for.

Given the breadth of the topic, the course cannot be comprehensive, nor go in depth into each dimension and method. Instead, it will launch first explorations, give some tools to navigate disciplinary and interdisciplinary knowledge, and, hopefully, the willingness to explore further and build one’s own path in our common future. The course aims to demonstrate how sustainable development concerns all sciences, research, and engineering. It also shows how the construction of responses and transformations represents challenges for science, research, and engineering. It will give a glimpse into some disciplines’ methods, but it is also resolutely multidisciplinary, and its structure aims to build cross-cutting visions between disciplines and themes.

Mastering the transformation of organic matter is key to tackle societal challenges such as the synthesis of new pharmaceutical drugs, the design of functional polymers and the recycling of wastes to value-added products. CHE_3S002_EP is an intermediate–level chemistry course that introduces the reactivity and transformation of organic chemicals, based on quantum chemistry. From the description of the electronic structures and bonding interactions in molecules (using molecular orbitals and Hückel theory), the transformation of organic and inorganic compounds is introduced, as well as the reactivity of organic functionalities (carbonyls, alkenes and aromatics) and the concepts of catalysis. This interactive course explores these topics through lectures, tutorials and labs.

Are you interested in the major challenges of the energy transition, health and the environment? Do you wonder about the sovereignty of technologies and materials? Then the “Chemistry for future leaders” course is for you! Why should you take it? Because chemistry is essential in all these areas, both for arbitration and for action.
In order to offer you the most relevant course possible, we have called on key players from the worlds of business, politics and senior civil servants. We asked them to share their experience and their needs in the field of chemistry. Drawing on our expertise as teachers and the testimonies of ministerial advisors, senior executives from major groups and members of the French government, we have designed a course that will put you in the shoes of decision-makers. You'll learn how to position yourself and arbitrate on complex issues involving chemistry.
The aim of this course is to provide you with a “survival kit for arbitration and action”. We'll teach you the fundamental concepts you need to know, without getting bogged down in details. And we'll give you the keys and tools you need to make informed decisions on major societal and industrial challenges.

The course runs over 10 weeks and includes lectures and tutorials. It is open to all and has no prerequisites. Our aim is to teach you a pragmatic and operational approach to chemistry.

Each lecture is built around a major social issue. These topical issues enable us to draw on the theoretical concepts needed to understand the subject in detail and provide answers to the case study. For each course, we will define a list of skills to be developed and assessed at the end of the period.
For example, the first courses deal with energy, and aim to develop a critical eye for the contribution of chemistry to the energy transition:
- Why have we become “fossil fuel addicts”?
- What are the possible alternatives? Solar, nuclear?
- Why does the ideal battery - one that is durable, light, safe and quick to charge - still not exist?

Of course, we won't stop at energy issues, because chemistry is everywhere. We'll also be looking at how to deal with critical metals and the impact of plastic waste on the environment and health. 
In lectures, we'll be doing practical exercises and role-playing. You'll be put in the position of decision-makers through practical case studies and serious games. You'll adopt different points of view and roles. For example, you'll have to assess an energy scenario, evaluating the risks and opportunities associated with materials or resources. To do this, you'll combine concepts learned in class.
Assessment will be continuous, with a final exam. Skill acquisition will be assessed through individual assignments and group analysis.
This course is without precedent at X or in the network of engineering schools. It provides a minimum knowledge base in chemistry, essential for your future career. This may be your last chemistry course, but it's one you won't want to miss!

The objective of the tutored project for the engineering students is to get more involved in a research project with the help of a tutor in the research center. This project spans the two periods and can be combined with the experimental EAs. This project can possibly replace a course module or an additional PREX. All areas of expertise in chemistry of the research center are concerned: materials science, organic chemistry, organometallic, coordination chemistry, analytical and theoretical chemistry. The subjects cover broad themes, for energy, the environment, innovative materials, chemistry and health, quantum technologies, molecular chemistry, catalysis ...

This internship option in "Chemistry for Energy and Sustainable Development" aims to immerse you in the field of chemistry research, in connection with current energy and environmental challenges. The proposed topics cover fundamental and applied aspects, aiming to understand and optimize chemical processes for the development of sustainable energy solutions.

The themes addressed may concern the chemistry of materials for energy storage and conversion, clean process chemistry, electrochemistry, catalysis, green chemistry, or waste valorization. The research conducted as part of these internships is often oriented towards potential applications, with a perspective of developing innovative and environmentally friendly technologies. The topics may be related to current socio-economic and environmental issues, such as the energy transition, the reduction of greenhouse gas emissions, or waste management.

Students will have the opportunity to explore various techniques and domains of chemistry for energy and sustainable development, including:

• Applied electrochemistry for energy storage and conversion systems, such as batteries, fuel cells, and electrolyzers. Students will be able to study electrode materials, electrolytes, and electrochemical processes to optimize the performance of these devices.
• Molecular modeling and computer simulation to predict the properties of materials and chemical processes. Students will be able to use modeling tools to design new materials and optimize synthesis and transformation processes.
• Energy materials, such as electrode materials, catalysts, absorption materials, and thermoelectric materials. Students will be able to study the physical and chemical properties of these materials and explore new synthesis and characterization strategies.
• Environmental chemistry, including the detection and quantification of pollutants, CO2 capture and storage, and pollutant degradation. Students will be able to study the chemical processes involved in the formation and degradation of pollutants, as well as remediation strategies.
• Process chemistry and biomass valorization, including the conversion of biomass into biofuels, chemicals, and materials. Students will be able to study thermochemical and biological biomass conversion processes, as well as product separation and purification strategies.

Students will also have the opportunity to use advanced characterization techniques to study the properties of materials and chemical processes, such as various spectroscopies, microscopy, electrochemistry, or X-ray diffraction.

Types of internships: internships can take place in France or abroad, in an academic or industrial context. For example:

• In the research center at the École polytechnique: LPMC, LPICM, LCM, IPVF
• In university research laboratories: Université Paris Saclay, ENS, Collège de France, CEA, etc.
• In companies in the energy sector: TotalEnergies, Engie, Orano, etc.
• In start-ups specializing in green technologies
• In industrial R&D centers in France or abroad

Information is available on the moodle page of CHI592, with internship proposals received by the department, links to X-Job board and the Career center.

Mastering the transformation of organic matter is key to tackle societal challenges such as the synthesis of new pharmaceutical drugs, the design of functional polymers and the recycling of wastes to value-added products. CHE 302 is an intermediate–level chemistry course that introduces the reactivity and transformation of organic chemicals, based on quantum chemistry. From the description of the electronic structures and bonding interactions in molecules (using molecular orbitals and Hückel theory), the transformation of organic and inorganic compounds is introduced, as well as the reactivity of organic functionalities (carbonyls, alkenes and aromatics) and the concepts of catalysis. This interactive course explores these topics through lectures, tutorials and labs.

Nowadays, we have access to large datasets, many created and released by governments. For example, here in France, we have the data.gouv.fr portal.

These datasets offer great insight into our societies and can help spot social trends or social issues.

During this modale, you will familiarize yourself with notions and tools for exploring data. We will discuss impactful research articles that use computational methods to uncover social issues. This class also introduces the different significant steps a data science engineer needs to know to extract knowledge from large volumes of data.

The first five sessions are dedicated to presenting concepts and tools, while in the remaining sessions, you will carry out projects in pairs with the tutor’s help.

Prerequisite: Python
Language: The materials are in English, but the class can be in English or French, depending on the students.

This page is for the Research Projects of the tracks "Algorithms and Foundations of Programming Languages".

Below you will find project proposals for 2017-2018

- Pierre-Yves Strub. A COQ Proof-Mode for APRHL

- Grégoire Lecerf. Factorisation des polynômes sur les corps finis.

- Grégoire Lecerf. Implantations HPC des opérations arithmétiques sur les polynômes et séries de petites et moyennes tailles.

- Olivier Bournez. Modèles de calculs continus: A propos de la puissance des modèles de calcul basés sur les équations,différentielles ordinaires.

Below you will find INF513 projects that were done in the previous years. We advise the students to contact the lecturers in charge of your favourite courses to discuss the possibility of doing a project under their supervision, or contact the supervisors that proposed projects this year or in the past.

====

- Dale Miller, Certificates for CTL Model Checkers.

- Stéphane Graham-Lengrand and Assia Mahboubi, Combination of decision procedures in presence of meta-variables (attached)

- Benjamin and Carola Doerr, Analyse des algorithmes  évolutionnaires (http://people.mpi-inf.mpg.de/~doerr/projet_approf_doerr_x13_ea.pdf)

- Tomer Libal and Dale Miller (shaolintl@gmail.com), Checking Proof Certificates (ProofCert project)

- Xavier Allamigeon (Xavier.Allamigeon@inria.fr), Falsifier formellement la conjecture de Hirsch.

Course Syllabus

• Data Modeling: ER model, Relational Model
• Relational Algebra, Relational Calculus
• SQL (Structured Query Language)
• Schema Refinement and Normal Forms
• Disks, Files, Buffers
• Tree- and Hash-Structured Indexes
• Evaluation of Relational Operators (selection, join, group-by aggregation, sorting)
• Relational Query Optimization (query plans, algebraic equivalence, plan space, cost estimation, search algorithm)
• Transaction Management
• Concurrency Control

Link to the course's web page: click here

Objectives:

Topological Data Analysis is an emerging trend in exploratory data analysis and data mining. It has known a growing interest and some notable successes in the recent years. The idea is to use topological tools to tackle challenging data sets, in particular data sets for which the observations lie on or close to non­trivial geometric structures that can fool classical techniques. Topological methods are indeed able to extract useful information about these geometric structures from the data, and to exploit that information to enhance the analysis pipeline.

Suggested readings:

Herbert Edelsbrunner and John Harer, Computational Topoogy: An Introduction, AMS press
S. Oudot. Persistence Theory: From Quiver Representations to Data Analysis. AMS Surveys and Monographs, Vol. 209, 2015
James R. Munkres. Elements of Algebraic Topology. Perseus, 1984

Language: The course material is in English. Lectures can be taught either in French or in English, at the students' convenience.

Evaluation: Final written exam, plus possibly one graded lab session.

Prerequisites :

in mathematics: a fair knowledge of linear and bilinear algebra, plus some notions of general topology. A background in statistics (MAP433) is desirable but not mandatory.

in computer science: some knowledge of algorithms (INF421) and programming (INF431 or INF442 or modal INF474A).

Feedback from this year's experience: if you are from MP, then this course is for you; if you are not from MP, then this course is also for you, although you will have to work harder; in any case, the goals remain achievable and are worth the effort! You can visit the course's webpage for further information, or contact the coordinator if you have any questions or concerns.

Computer-driven control of physical systems is at the center of the emerging field of cyber-physical systems, among which autonomous systems. These systems are most often critical in terms of safety or cost. A challenge is the increasing use of artificial intelligence, whether for perception or control.

Mastering the modeling, control and verification of such systems is crucial to guarantee their functionality and reliability. The course aims at both introducing the theoretical background and exploring some practical cases.

The aim of this course is to study the securing of Information Systems in the open network communication setting. Through practical cases, the course will show many existing threats and address current techniques to circumvent them. 

Requirements: INF558 (Introduction to Cryptology), INF557 (From the Internet to the IoT: The Fundamentals of Modern Computer Networking).

Evaluation mechanism: This course will be evaluated by way of challenges prepared during labs and a final exam

Language: english slides, english/french speaking

Advanced Deep Learning 

Deep learning has revolutionized the field of artificial intelligence and has become a critical tool in numerous applications, such as computer vision, natural language processing, graph representation learning and speech recognition. The field of deep learning is still constantly evolving with new techniques and architectures being developed at an immense pace. In this context, it is essential for aspiring deep learning practitioners to stay up-to-date with the latest advances in the field.

The class will be evaluated with a combination of assignments, team projects and a student challenge. More details will come. 

Research internship in Data Science

Research internships in Data Science cover a wide range of varied questions, illustrating the importance and diversity of contemporary researchs in AI, Machine Learning and Bigdata. These questions vary from theorical problems in which students sometimes respond in an innovative way, to industrial applications, but always with a strong scientific or technological dimension.

The interships proposed come from a large demand in the best international academic and industrial research centers. They enable to understand innovative developments, in particular in the industrial world, most of the time based on a solid body of theorical knowledge. They also enable to understand the complexity - historically unprecedented - of the informatics systems built today. Thus, behind an ordinary processor lies the entire computerised production chain, from modular design to mask design, including algorithms for symbolic proof of circuits. Similarly, the complexity of writing software that has to run simultaneously and in a coordinated way on several thousand machines is of such a nature that it is impossible to hope for correct operation without a systematic methodology.

Students interested in a career in research in this field will find material to confirm their vocation for a specific field and they will discover laboratory's life. The other students will be able to get acquainted with the research and innovation world, almost all of them will have to deal with in one way or another during their career. This internship will also be an opportunity for some students to choose research-based training, attested by a doctorate, which is often the reference diploma in the global computer industry.

It is highly recommanded to have taken one of the in-depth programs (PA) in Data Science proposed by the Informatics Department to enjoy this internship.

Required level: M1 in Computer Science or equivalent
Evaluation modalities: internship dissertation with a defense in front of a board.

This course will cover fluctuations, unemployment, economic crises, and macroeconomic stabilization policies through the lens of the “New Keynesian” model that has developed over that past couple of decades and now guides short-run macroeconomic analysis. After reviewing the building blocks of the short-run macroeconomic model (namely, aggregate demand and supply), we will cover conventional monetary and fiscal policies, and then turn to the unconventional policies that are put in place during “liquidity traps”, i.e. situations wherein conventional monetary policy is unable to efficiently restore aggregate demand (as is currently still the case in the euro area). We will occasionally look into the historical record - from the Great Depression to the Japanese experience, to the worldwide Great Recession - and structure the evidence by means of a simple macroeconomic model with price rigidities. We will discuss the effectiveness of unconventional monetary policies (forward guidance, quantitative easing), as well as the unconventional effects of fiscal policies, during liquidity traps. Finally, we will examine whether the current trap follows from a serious but temporary shock or reflects a “secular stagnation" episode of persistently low aggregate demand and growth.

Prerequisite

Intermediate Macroeconomics course (Bachelor, Year 2)

Readings

Main text: Edouard Challe, Macroeconomic Fluctuations and Policies, MIT Press, 2019

A complementary reading list of policy and accessible research papers will be provided in due time.

This course introduces students to the research frontiers in economics. Each week, a researcher from the laboratory CREST would present a central topic of his/her research. Students are expected to see how researchers tackle problems using the tools and concepts developed in economics. Topics include traditional microeconomics, macroeconomics, and econometrics, as well as recent interdisciplinary developments such as blockchain technology, and machine learning.

The Valuation for Startups course provides students with a comprehensive understanding of how early-stage venture capitalists and investors value companies. Throughout the course, students will explore both the theoretical and practical aspects of startup valuation, gaining insights into the unique factors that influence the value of high-growth, early-stage businesses.

This course will guide students through key topics such as understanding what defines a startup, how venture capitalists assess potential investments, and the different valuation methods tailored specifically for startups. Additionally, the course will cover strategies for adjusting valuations over time, developing a successful startup portfolio, and analyzing a real-life case study with an entrepreneur. Students will gain practical knowledge that can be applied to their own startup ventures or investment decisions.

By the end of the course, participants will be able to:

•Understand the core components of what makes a startup attractive to venture capitalists.

•Apply enterprise valuation methods to startups, considering growth potential and risk factors.

•Recognize how valuations evolve over time as startups scale.

•Explore portfolio creation and investment strategies in the startup ecosystem.

Whether you’re an aspiring entrepreneur, venture capitalist, or business professional, this course offers valuable insights into the dynamic world of startup valuation.

Key Topics Covered:

1. What is a Startup and What is a Venture Capitalist?

•Understand the defining characteristics of startups and how they differ from traditional businesses.

•Explore the role of venture capitalists in funding and scaling startups.

2. How Are VCs Assessing Startups?

•Discover the criteria venture capitalists use to evaluate startups, including team, market opportunity, product, and traction.

•Learn how VCs balance risk and reward in their investment decisions.

3. Introduction to Enterprise Valuation

•Gain a foundational understanding of general enterprise valuation methods, such as discounted cash flow (DCF) and comparable company analysis (CCA).

•Understand the traditional factors that influence a company’s valuation.

4. Enterprise Valuation Applied to Startups

•Learn how traditional valuation methods are adapted for early-stage companies with little revenue or profits.

•Explore startup-specific valuation techniques, including the venture capital method and risk-adjusted methods.

5. How to Change Valuations Over Time and Portfolio Creation

•Analyze how startup valuations evolve as they hit key milestones, scale operations, and expand their market presence.

•Understand how to build a balanced portfolio of startups to manage risk and maximize returns.

6. Case in Point: Real-Life Example with an Entrepreneur

•Study a real-world case involving an entrepreneur, examining how their company was valued and funded.

•Gain practical insights from the challenges and successes faced by the startup during its fundraising journey.

Who Should Take This Course?

This course is ideal for:

•Entrepreneurs looking to understand how their startup will be valued by investors.

•Aspiring venture capitalists and investors who want to learn how to evaluate and invest in early-stage companies.

•Business professionals or students interested in startup ecosystems and venture capital.

No prior knowledge of finance or valuation is required, but a basic understanding of business concepts will be beneficial.

ECO 583 Business Economics

The objective of this course is to study business cases in which professionals take decision mobilizing economics and data. Sessions are devoted to different topics presented by a professional expert of the subject. Students also present business issues.

As an example, the calendar of last year :

• January 8th :  Rémi Avignon – Course Introduction and Values Chains
• January 15th : Jean Baptiste Vilain – Auctions
• January 25th : Rémi Avignon and Thomas Larrieu – Platforms
• January 29th : Olivier Beaude and Paulin jacquot – Electricity Markets
• February 5th : Arthur Souletie – Data and Health
• February 12th :  Nicolas Dupuis – Pricing
• February 26th : Julie Tisserond – Data Strategy
• March 4th : Students Presentations
• March 11th : Students Presentations

Evaluation is a combination of the three following points:

• Presence is mandatory for each course. A significant part of the grade will depend of assiduity and activity during the courses.
• During each session, a group of students will discuss the day's presentation.
• Each student must discuss one research paper on a business case during the semester.
• During the two last sessions, groups of students will present business cases prepared during the semester.

Cours en anglais

Crédits ECTS : 4

The complexity of the socio-economics systems and their issues (biodiversity, climate, development, inequalities, food safety...) call to an interdisciplinary approach to better understand, and identify or build a set of possible responses. This need of crossed perspectives, from key concepts and disciplinary methods, becomes apparent once we confront concrete practical cases.

With this mind, we offer a 3-yeay course unit (UE) aimed to develop the crossed perspectives on environmental issues throught study of territories. The UE itself is the result of a interdisciplinary construction work between biologists, chemists, climatologists, ecologists and economists. The cours is designed to be taught by teachers of these various fields. To ensure the study of practical cases, we focus on one theme - land uses and land use planning (or not) - and one area - Ile-de-France - involving processes, heterogenous and independent environments and actors at different scales (In 2022/23, the practical case was on the plateau de Saclay development, but it could change from one year to the next).

The first class will be an introduction of the theme of land use et their issues, interdisciplinary frameworks and the case study. Each of the 4 next classes will be organized in a in-depth theme lecture hall, according to the field (economics, ecologics, chemistry, climate) fllowed by a short class in the form of an analysis of the case study or a similar one. An extra class will be focused to the involved actors in the controversy and governance issues. The rest of the course will be organized around group projects to answer a problem of the case study precised by students.

LINKS BETWEEN THE COURSE AND SUSTAINABLE DEVELOPMENT GOALS (SDGs)

This course focuses directly on the following sustainability issues:

• SDG 9 Build a resilient infrastructure, promote a sustainable industrialization that benefites everyone and incite innovation
• SDG 11 Ensure cities and human settlements are open to everyone, safe, resilent and sustainable
• SDG 15 Preserve and restore terrestrial ecosystems, ensuring sustainable use, sustainable forest management, desertification, and reversing the soil deterioration process and put an end to the biodiversity loss.

How the course take those issues into account?

The overall objective of the course is to deploy and cross interdisciplinary perspectives on socio-ecological issues throught study of territories. More precisly, it aims to develop skills of analysis and assessment of wether or not sustainable land use planning is or might be. The aim is to ensure that ecological (climate, biodiversity, pollution...), economical (employment, transports, infrastructures...) and social (quality of life, inequalities...) issues are taken into consideration. As such, the course not only directly focuses on various SDGs, but also seek to articulate them.

Traffic and Transportation systems in urban contexts

M. Benoit Vedel (DG Aimsun), M. Xavier Boulet ( chargé d'études Aimsun) 

The level of traffic in cities has increased significantly over the last decades. Such level of trafic has a considerable impact on the quality of life for all citizens and economic growth.

 Balancing the demand for increasing personal mobility and economic growth, with the need to respect the environment is a real challenge. The link between transportation networks and economics is manifold both at the macro and micro level. Value flows on the transport network are capitalized into land values, economic recessions stall the mobility of people and goods, higher-income households travel more frequently, and so on.

The objective of this course is to discuss those aspects and provide a set of tools and possible solutions for different urban settings.

I- 4-step modeling

II- Fundamentals on traffic systems

III- Active traffic management strategies

IV- Traffic simulation (Aimsun software)

V- Cost-benefit analysis: a powerful tool for decision makers

This course will cover fluctuations, unemployment, economic crises, and macroeconomic stabilization policies through the lens of the “New Keynesian” model that has developed over that past couple of decades and now guides short-run macroeconomic analysis. After reviewing the building blocks of the short-run macroeconomic model (namely, aggregate demand and supply), we will cover conventional monetary and fiscal policies, and then turn to the unconventional policies that are put in place during “liquidity traps”, i.e. situations wherein conventional monetary policy is unable to efficiently restore aggregate demand (as is currently still the case in the euro area). We will occasionally look into the historical record - from the Great Depression to the Japanese experience, to the worldwide Great Recession - and structure the evidence by means of a simple macroeconomic model with price rigidities. We will discuss the effectiveness of unconventional monetary policies (forward guidance, quantitative easing), as well as the unconventional effects of fiscal policies, during liquidity traps. Finally, we will examine whether the current trap follows from a serious but temporary shock or reflects a “secular stagnation" episode of persistently low aggregate demand and growth.

Prerequisite

Intermediate Macroeconomics course (Bachelor, Year 2)

Readings

Main text: Edouard Challe, Macroeconomic Fluctuations and Policies, MIT Press, 2019

A complementary reading list of policy and accessible research papers will be provided in due time.

This course introduces students to the research frontiers in economics. Each week, a researcher from the laboratory CREST would present a central topic of his/her research. Students are expected to see how researchers tackle problems using the tools and concepts developed in economics. Topics include traditional microeconomics, macroeconomics, and econometrics, as well as recent interdisciplinary developments such as blockchain technology, and machine learning.

In order to complement theoretical knowledge acquired during the courses, Project ECO511 provides students opportunities to work on a topic in applied economics, with some empirical ingredients or applied economic theory. Students work in a group of two or three members, and they will be graded during an oral exam in March. A written report should be submitted a week before the oral exam. The academic tutor is supposed to provide a topic, and meet the students at the beginning to help starting the project, and expected to be available for a help from October to March. The list of topics will be provided at the end of September. The allocation of the students will be on the first-come-first-serve basis.

https://sites.google.com/site/geoffreybarrows/courses/applied-project-eco511

ECO 567b Traffic and Transportation systems in urban contexts

Aurore Remy (TSS, Aimsun); Zoi Christoforou (Laboratoire Ville Mobilité Transport, ENPC)

The level of traffic in cities has increased significantly over the last decades. Such level of trafic has a considerable impact on the quality of life for all citizens and economic growth.

 Balancing the demand for increasing personal mobility and economic growth, with the need to respect the environment is a real challenge. The link between transportation networks and economics is manifold both at the macro and micro level. Value flows on the transport network are capitalized into land values, economic recessions stall the mobility of people and goods, higher-income households travel more frequently, and so on.

The objective of this course is to discuss those aspects and provide a set of tools and possible solutions for different urban settings.

I- 4-step modeling

II- Fundamentals on traffic systems

III- Active traffic management strategies

IV- Traffic simulation (Aimsun software)

V- Cost-benefit analysis: a powerful tool for decision makers

The course is meant to provide a contextual history of how economists have  approached, and sometime modelled “nature” and “the environment” in their work. It  emphasizes big shifts in which aspects of nature became of interest in the past century for societies at large and for various species of scientists and economists (end of fossil energy, pollution, biodiversity, global warming, planetary boundaries). We cover the tools and models economists developed to solve issues raised by nature (since it was mostly modeled as a constraint or issue), and how these tools were applied, discussed and challenged in academic, policy and business spheres since World War II.

We cover the history and controversies around models of growth, climate models including IAMs, cost-benefit analysis, contingent valuation, valuing ecosystem services, carbon taxes, cap and trade markets, commons governance, market failures, social cost of carbons, redistributive effects of climate policies, etc. We adress the theoretical, empirical, but also ethical and political controversies surrounding these tools, their efficiency, fairness and political acceptability (for instance the discounting of future generations, or how cost-benefit analysis was used to support or resist international treaties on the regulation of carbon emissions). 

The course is open to students with a background in economics, as well as engineering/science students with no background in economics who consider working in environmental sciences, expect to be confronted with economic ideas and models and would like to understand their origins and dissemination better. The course is centered on economists, the models and tools they produced, but brings in both mainstream and heterodox perspectives, and details pushbacks from other sciences, natural, life and social,from legal scholars, and from civil societies.

EDACF 1 & 2, SEF, SCUP 1 Seminar « Economics and Finance »

The goal of this seminar is to invite professionals from the public, finance, service and manufacturing  sectors, to make a presentation of their business and industry. Students make an introductory lecture (30 min) on the theme of the session (by group of maximum 3 persons), and prepare the discussion after the professional’s presentation. At the end of the semester, SEFstudents must also write a thesis on one of the themes of the seminar

Autres dates : non scup: 22/10, 12/11, 26/11, 3 /12 , 10/12 scup: 10/12 , 5/11

1. (scup/m1m2edacf) Introductory lecture : P. Crifo  / G. Hollard, 17/9

2a. (scup/m1edacf). Corporate finance: G Mailly (JP Morgan), 24/9

3a. (scup). Housing and cities: A Briant (Mairie Paris), 1/10

3b. (m1edacf). Insurance (1): K.Dedieu (Axa), 1/10

4(m1edacf). The finance industry: JM.Beacco (ILB), 15/10

5(m1edacf). Trading: A.Levy Rueff (Exotikequation),  5/11

6a(scup/m1edacf). Smart cities: S De Guio (Schneider electric),  12/11

6b (m2edacf). Corporate finance: Estin 1? , 12/11

7a (m2edacf). Regulating finance: V.Berger (Banque de France), 19/11

7b(scup). Data and urban services: N.Augris (Arep), 19/11

8a (m1m2edacf). Corporate finance: Estin 2?, 26/11

8b (scup). Health &pollution : Nhân Pham Thi (Institut Pasteur), 26/11

9. (scup/m1edacf). Insurance (2) :  R.Lemarchand (Generali), 10/12 

10 (scup/m1m2edacf). Smart mobility:  D Gance (Diginove consulting), 14/1

11a (m2edacf) Financial products: M.Florig (Credit Agricole), 21/1

11b (scup). Smart energy : Franck Chevalley (Atos Worldgrid): 21/1

Description and references

Corporate finance: GMailly (JP Morgan)

Housing and cities: A Briant (Mairie Paris)

Title: segregation in cities

The lecture will examine social and ethnic segregation in modern metropolitan areas, with a special focus on French cities. The costs and benefits of urban segregation will be discussed from an economic point of view, building on simple urban economic models. Empirical analysis on educational and employment outcomes of segregated minorities will be presented, with a special emphasis on the French « banlieues ». Reinforcing the social mix of neighborhoods or offering moving opportunity to segregated people are at the heart of various public instruments. In France, the efficiency of social housing policy (SRU law) and actions in favor of separated suburban areas (politique de la ville) will be questioned using this methodological background.

Articles :

Are ghettos good or bad ?, David M. Cutler and Edward L. Gleaser, The Quarterly Journal of Economics, 1997 (http://www.csus.edu/indiv/c/chalmersk/econ180fa08/cutlerglaeser1997.pdf)

Ethnic segregation and ghettos, Axel Anas, A Companion to Urban Economics, Blackwell publishers, Richard Arnott and Daniel McMillen, editors.  (https://sites.google.com/site/alexanashomepage/selected-publications/2005.%20ANAS.%20Ethnic%20Segregation%20%26%20Ghettos.%20Chapter%20in%20Companion%20to%20Urban%20Economics.%20An%20Undergraduate%20Reader..pdf?attredirects=0&d=1)

Housing policy : Low-Income Households in France, Anne Laferrère et David Leblanc, A Companion to Urban Economics, Blackwell publishers, Richard Arnott and Daniel McMillen, editors.

(http://www.crest.fr/ckfinder/userfiles/files/Pageperso/laferrere/laferrere_fichiers/ACTC10.pdf)

Insurance (1): K. Dedieu (Axa Corporate Solutions)

Title: Insuring climate risk and natural disasters : the impact of big data

Heat waves, cyclons and other climate disasters are increasing with climate warming and threaten the most vulnerable countries. The diffusion of new technologies and new data allow a better understanding of such risks and widen the frontier of what is insurable

Reference

Munch Re. 2017. Natural catastrophes 2016.

https://www.munichre.com/site/touch-publications/get/documents_E-271800065/mr/assetpool.shared/Documents/5_Touch/_Publications/TOPICS_GEO_2016-en.pdf

Complementary references (optional)

Caisse centrale de reassurance. CatNAT expertise dédiée à la connaissance des risques

Régime des catastrophes naturelles

The finance industry: JM.Beacco (ILB)

Title: Risks in the Banking Industry

Business globalization, new emerged economic areas, multinational corporate firms and euro zone indebted states have generated an increasing banking credit exposure whilst simultaneously, financial markets innovation eases risk transfer through markets. This “marketisation” of risks, notably credit risk, generated a systemic risk that led to 2008 crisis and maintains a high volatility. Regulators ask for more control and better risk management in order to prevent future crisis.

The introductory presentation by students should be a short brief around this topic and present thei opinion and recommendations on “how to better manage risks in the banking industry” today and tomorrow.

References

The role of ratings in structured finance: issues and implications: http://www.bis.org/publ/cgfs23.pdf

Ratings in structured finance: what went wrong and what can be done to address shortcomings: (http://www.bis.org/publ/cgfs32.pdf?noframes=1

Risk Management Lessons from the Global Banking Crisis of 2008: http://www.sec.gov/news/press/2009/report102109.pdf

Report on issues regarding the valuation of complex and illiquid financial instruments http://www.eba.europa.eu/documents/10180/592844/20080618b_valuation.pdf

OCC supervisory guidance on model risk management http://www.occ.gov/news-issuances/bulletins/2011/bulletin-2011-12a.pdf

PWC Risk in Banking http://www.pwc.com/en_GX/gx/banking-capital-markets/banana-skins/assets/pwc-banking-banana-skins-2014-v2-april.pdf

Complementary references (optional)

Hull (John): risk management and financial institutions, Pearson 2013 3rd edition

De Servigny (Arnaud), Zelenko (Yvan), Le risque de crédit : nouveaux enjeux bancaires, Paris, Dunod 2003, réédition 2010

Beacco (Jean-Michel) et Hubaud ( Benoît), Titrisation : Maillon clé du financement de l'économie, Paris, Eyrolles, mars 2013

Brealey (Richard A), Myers (Stewart C.), Allen (Franklin), Principles of Corporate Finance, Mc Graw Hill, last edition, Chapters on the International Finance (27 and 28)

Trading: A.Levy Rueff (Exotikequation)

Title: From the open outcry market to DeepMind: the great upheaval

The golden age of 'locals' (independent traders dealing on the physical floors of the exchanges) was only 25 years ago. At the outcry, we used to price and hedge products such as options interpolating reference prices printed on paper sheets. Since then, we have transitioned to the comfort of dealing rooms, assisted by computers. Their roles are getting bigger along with technological progresses and in many cases, trading robots are even becoming autonomous. This evolution is both an opportunity and a challenge for traders as it radically shifts the field of skills both human and technical. As such, this conference aims to help students rethink their value added in the business. Having started his professional career at the outcry, been an “old school” trader and transitioned to systematic trading, the speaker will share his inside with the students.

Based on the following readings, the introductory speaker will summarize his/her understanding of what are the main skills to be successful in trading.

References

Reminiscences of a Stock Operator  - Edwin Lefèvre

A roman a clef, it is the first best seller about the stock markets written back in 1923

Market Wizards: Interviews With Top Traders Updated - Jack D. Schwager 

Interview of several legendary traders detailing their thinking process.

Smart cities: S De Guio (Schneider electric)

Sustainable urban development is a key issue for the future of the planet. With more than 50% of the world's population, cities are already responsible for more than 70% of greenhouse gas emissions. Buildings alone represent more than a third of the world's energy consumption. To face these environmental and social challenges, cities will have to develop smarter and flexible infrastructures, from connected building to the ecodistrict.

References

 --World Energy Outlook 2017. International Energy Agency. (Navigate on line)

Complementary references (in French)

--Www.smartgrids-cre.fr

--Etude sur les perspectives stratégiques de l'énergie. Monographie n3 sur les réseaux électriques. E-Cube strategy consultants.

—PCM - la revue ponts et chaussées - décembre 2016, Smart Grids

--Rifkin Jeremy. La troisième révolution industrielle. Les liens qui libèrent, 2012.

Regulating finance: V.Berger (Banque de France)

Title: Bank liquidity risks and supervision

Communication in the media about the supervision of liquidity risks faced by banks insists a lot on prudential rations, that is on the necessity for banks to be correctly capitalized. We hear less about liquidity risks though they have played a major role in bank failure and bankruptcy

References

*prudential requirements for credit institutions and investment firms and amending Regulation (EU) No 648/2012" :  articles 411 to 428

* Basel III: The Liquidity Coverage Ratio and liquidity risk monitoring tools

http://www.bis.org/publ/bcbs238.pdf

* Rama Cont Central clearing and risk transformation

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2919260.

* "Le scandale Dexia, "Enquête sur la plus grosse faillite bancaire européenne", Alain Piffarretti, 2013;

Smart mobility: D Gance (Diginove consulting)

Title: Smart Mobility

Smart mobility has to bring efficient answers to the economic, social and environmental challenges of megacities. Today because of the emergence of digital technology (i.e. new technologies and smart information systems) the ways of transportation have evolved to take into account people motivations and other factors such as consumption, eco-responsibility, social link, economic development of a territory...

They concern Local Authorities for governance as well as suppliers in connection with mobility of people and logistics. Among the technologies that have the greater impacts on performance, customer perception and new trades we shall study in particular the development of mobile Internet and 5G network, Big Data and Artificial Intelligence, cashless payment, autonomous vehicles and intelligent infrastructures during this Masters’ degree.

For the introduction, students can focus on the following question: Regarding intelligent infrastructures in Smart Cities what would be their main characteristics for Smart Mobilities in order to be operated in an Infrastructures-as-a-Service (IaaS) mode ?

References :

C. Benevolo, R. Dameri , B. D’Auria (2016). Smart Mobility in Smart City. Action Taxonomy, ICT Intensity and Public Benefits in T. Torre et al. (eds.), Empowering Organizations, Lecture Notes in Information . Systems and Organisation 11, DOI 10.1007/978-3-319-23784-8_2

Urban mobility in the smart city age. Smart Cities cornerstone series

Website: https://amsterdamsmartcity.com/themes/mobility

Financial products: M.Florig (Credit Agricole)

Title: Interest rate derivatives and currency derivatives

The seminar will cover the topics of interest rate derivatives and currency derivatives, focusing on the way markets have changed sine the financial crisis driven by regulation, central bank intervention and supply and demand dynamics

An introductory presentation by students could cover for example

·         OIS discounting

·         short term interest rates incl. differences in their construction (LIBOR, Eonia, repo, gvt rates)

·         swaps / new issue swaps

·         fx forwards

Reference

John C. Hull, Options, Futures and Other Derivatives, 2015 

(book bought and lended by the department)

Health & Pollution: N. Pham Thi (Institut Pasteur)

Title: Air pollution, the silent killer and money spoiler: how to quantify this new plague?

How to define the air pollution? What are the best markers? 

How can we measure the consequences of this co-factor on human diseases? 

Explain the different points of view? Describe the tools

Imagine new techniques to measure and to estimate the costs of air pollution on human health. 

Insurance (2) :  R.Lemarchand (Generali)

Title: Cyber criminality and insurance

Cyber criminality is a fast growing phenomena with large impacts for individuals, corporate companies, public institutions or even security of states.

This is a new challenge for the insurance industry: understand the risks, develop prevention tools and build assistance and insurance solutions.

References :

- Cyber-threats and trends : https://www.enisa.europa.eu/publications/enisa-threat-landscape-report-2016

- WannaCry ransomware attack : http://www.ey.com/Publication/vwLUAssets/ey-wannacry-ransomware-attack/$File/ey-wannacry-ransomware-attack.pdf

Smart grids and energy: F. Chevalley (Atos worldgrid)

Title: Smart cities and smart grids

References:

·         http://www.smartgrids-cre.fr/index.php?p=smartcities-caracteristiques

·         https://setis.ec.europa.eu/energy-research/sites/default/files/library/ERKC_PB_Smart_Cities.pdf

Complementary readings:

·         Blog  : http://www.smartcitiesbymachnteam.com/fr/2018/05/21/les-villes-lieu-de-concentration-extreme-des-enjeux-energetiques/

Differential manifolds are geometric objects locally described by coordinate systems (real or complex), but possessing a global structure that can be particularly intricate. These objects arise naturally in mathematics and also serve as the framework upon which many Physics theories are built (general relativity, gauge theories, etc.).

This course is divided into two parts.

The first part is an introduction to differential manifolds and some of the key concepts associated with them (charts, atlases). We will start with the definition of abstract manifolds possessing a differential structure and provide examples of such manifolds, along with some recipes for constructing differential manifolds (quotient manifolds, connected sums, submanifolds, etc.). We will particularly focus on constructing 2-dimensional manifolds, which will give us a first glimpse of the complexity of manifolds. Once this general framework is established, we will introduce the notion of smooth maps between manifolds, as well as the concepts of embedding and submersion.

We will study the consequences of Sard's Theorem, which serves as the starting point for several developments, including Whitney's embedding theorems, which implies that (abstract) manifolds are not fundamentally more general than the simpler notions of submanifolds of Euclidean space. Sard's Theorem also forms the basis of the theory of transversality and intersection theory, which will lead us to the notion of the degree of a map defined between manifolds and the definition of the Euler characteristic of a manifold.

All these tools will give us the opportunity to approach Morse Theory, which allows for a better understanding of the topological complexity of a compact manifold by studying the critical points of functions. From this, we will derive Reeb's Theorem, which characterizes spheres.

Next, we will define and study bundles and sections of bundles, which are ubiquitous in geometry as well as in various physics theories. We will delve deeper into vector bundles, including the tangent bundle, cotangent bundle, and normal bundle. Studying the Hopf fibration (and its generalizations in higher dimensions) will help us better understand the challenges related to the classification of bundles.

Differential manifolds provide the natural framework for a rich integration theory. This theory, which relies on the notions of differential forms and exterior derivative, will provide us with a unified framework for defining the gradient, divergence, and curl operators, as well as the associated integration by parts formulas (Stokes' Theorem). We will also introduce some basics of de Rham cohomology, connecting with the course on algebraic topology.

The second part of the course builds upon the concepts developed in the first part. We will begin by defining the notion of a metric (Riemannian or pseudo-Riemannian) on a differential manifold. We will then introduce the Levi-Civita connection as an operator acting on sections of the tangent bundle, leading us to the notions of parallel transport and curvature (Riemann curvature tensor). We will define and study geodesics on a Riemannian (or pseudo-Riemannian) manifold, which will allow us to define geometric normal coordinates on a manifold.

In the context of Riemannian manifolds, we will define various notions of curvature: Riemann curvature tensor, sectional curvature, Ricci curvature tensor, and scalar curvature. We will particularly focus on the case of surfaces embedded in 3-dimensional Euclidean space, which will give us a better understanding of the notions of connection and curvature. Finally, we will state and prove some results regarding the links between curvature (especially its sign), topology, and geometry of Riemannian manifolds, such as the (Chern-)Gauss-Bonnet Theorem and Myers' Theorem.

Bibliography :

-- Manfredo P. do Carmo : Riemannian Geometry, Birkhäuser.
- Victor Guillemin and Alan Pollack : Differential Topology. Prentice-Hall.
- Morris W. Hirsh : Differential Topology, Springer
- Peter Petersen : Riemannian Geometry, Springer.

Course language: Textbook in english, Lectures in French or English

ECTS credits: 5

This course in an introduction to algebraic geometry and arithmetic geometry through the example of elliptic curves, that is non-singular plane projective curves given by a degree 3 equation. A remarkable property of elliptic curves is the existence of a group law on its set of solutions. The first part of the course will be dedicated to the the introduction of the language of algebraic varieties, and more precisely to Hilbert's Nullstellensatz and to projective geometry. Some examples related to Bezout's intersection theorem will be studied. The second part of the course will be dedicated to the properties of plane projective curves and more precisely of elliptic curves. The properties of elliptic curves will be studied over various fields: over the complex numbers, where elliptic curves can be identified to quotients of C by lattices; over finite fields, with Hasse's theorem which provides a bound on the number of points of such elliptic curves; and over the rational numbers, with the celebrated theorem of Mordell. The study of elliptic curves over finite fields will be illustrated with some applications to cryptography and to factoring algorithms. In the case of the field of rational numbers, some explicit examples in which the group of rational points can be computed will be studied.

Bibliography

Language of the course: French or English

Geometry.

Geometry studies topologic spaces with a supplementary structure: differential, riemannian, lorentzian, symplectic, holomorphic, algebraic, etc. Often based on physics, these structures in turn form the natural framework in which contemporary physics theories are formulated, especially when global phenomena are involved.

From a mathematical perspective, the structures concerned lead to as many branches of mathematics, which interact with each other in a multitude of ways and rely on a wide range of analytical, algebraic and topological techniques.

Thus, could be covered from the Riemannian geometry perspective, complex analysis, harmonic analysis and algebraic geometry. This applies more generally to complex geometry, which studies varieties defined by holomorphic functions.

Here are a few possible ideas for internships in these areas.

• Riemannian geometry: topology and bending.
• Gauge theory: the study of connections on a vector bundle, which constitute the natural framework of the Yang–Mills theory.
• Riemann surfaces:
• Hodge theory:
• Introduction to algebraic bending.
• Holomorphic functions of several variables and pseudoconvexity.
• Lamination and tissues.

Dynamical systems

The purpose of the dynamical systems is the study over a long period of a transformation acting on a space of configurations. Physical systems are often described by differential equations that lead to continuous flows and therefore a study of this kind. As a general rule, a differential equation cannot be integrated explicitly, we try to obtain qualitative information discretizing time. This leads us to consider discrete dynamic systems.
This two main categories are themselves devided into multiple subcategories depending on the nature of the transformation and the geometric structures it preserves (measurable, topological, differentiable, symplectical, holomorphic, algebraic). While this classification is of course very permeable, it does enable us to identify general concepts for each of the classes. But it is often the significant examples of new dynamic phenomena that ultimately guide the research. Here are a few ideas for internship topics.

• Symbolical dynamic. Space is a series of symbols from a finite alphabet, the change, difference of details. The properties of these series involve basic notions of ergodic theory such as entropy.
• Geodetic flow. It is a natural flow on all surface, which is particularly interesting to study when the bending is negative. Its dynamic enable to describe global geometric properties of the surface.
• Hamiltonian systems. These systems appear naturally in classical mechanics. Fine techniques allow either to build periodical orbits () or to describe their stability (KAM theorem).
• Dynamics in small dimension. The study of the family x⇒ax(1-x) on the interval [0,1] shows spectacular cascade bifurcations, whose study provides a good introduction to chaos, and to universality phenomena. This family spreads in dimension 2, and we can then observe strange attractors.
• Holomorphic dynamic. The thoery of iteration of polynomials in the complex plane is particularly rich, combining complex analysis and topology of plane compaxts. This theory is particularly visual, and many images of fractal can be obtained, whose interpretation is formidable.
• Algebraic dynamic. While the iteration of rational applications in any dimension is a field combining several dificult theories, some questions with digital aspects can be covered, such as the study of degree growth.

Course language: French

This course is a practical introduction to intellectual property law, information and technology law, designed especially for engineers and business people.

It is a global approach which helps students creating a new and strategic way of thinking when building or working on tech projects, by using law as a tool.

This course also gives students a better understanding of the legal implications of technology law and of the future challenges they will have to face while working in the tech industry.

Art history - what is a masterpiece?

           The notion of the masterpiece is one of the most widely used in everyday vocabulary, and generally designates a production considered as an ultimate and perfect achievement, endowed with universal resonance, in the field of artistic creation: La Joconde de Vinci, Hamlet de Shakespeare ou Le Penseur de Rodin among other examples.

Its contemporary extensions are abundant, and we can speak metaphorically of a sporting action, a mathematical demonstration or an entire existence as a "masterpiece", but the term nevertheless remains spontaneously attached to the aesthetic field.

Philosophical and semantic reflections on this term and what it covers have abounded since the 18th century, generally to "deconstruct" it to reveal a potentially abusive form of authority. They have also resulted in a monumental bibliography. In this seminar, we will attempt to reverse the usual, highly theoretical approach, and start from the objects themselves, usually considered "masterpieces" in the institutional framework and common perception, to detect the constituent elements that lead to this highly laudatory designation - and ultimately criticize them.

This approach will therefore be much more empirical and will enable us to familiarize ourselves with the methods of art history in the apprehension of its objects.

For each session, we'll take one or multiple case studies, following a chronological order, to gradually sketch out a general history of art (and painting in particular) in the modern West. These case studies will systematically stem from major public collections, to enable students to see the works in situ, at the Louvre, the Musée d'Orsay or the Centre Pompidou.

Evaluation will take the form of an in-class presentation or a written or video report.

Among the studies, we'll tackle: Titian's Le Concert champêtre; Michelangelo's L'Esclave mourant; Vermeer's L'Astronome; David's Le Serment des Horace; Monet's La Gare Saint Lazare; Degas' Le Ballet...

Evaluation methods :

Evaluation will take the form of an in-class presentation or a written or video report and be based on reading notes, oral presentations, and attendance.

Course language: French

The regain of international crises and violence explains today's high interest in international relations, which is reflected in public debate by experts in touch with current affairs - political scientists, sociologists, jurists, and geopoliticians... On the contrary, the contribution of history is rather neglected, even though it can "help us to think about the 'complexity' of international relations", as historian Robert Frank highlighted.

This is the ambition of this seminar, to build a framework for problematic reflection in a resolutely historical perspective centered on the short geostrategic 20th century. This century was opened by the First World War and closed by the turning point which, in 1989-1991, resolved the East-West antagonism by the disappearance of the East and the multiform hegemony of the American hyperpower confronted with the global disorder. However, the seminar will not stop from going back to the 19th century, to give a report on the history of globalization and successive European systems and to open up trails toward recent developments.

The approach will be based primarily on the achievements of the French school of international relations: first and foremost, the epistemological renewal impelled by Pierre Renouvin and Jean-Baptiste Duroselle, which transformed traditional diplomatic history into a total history, opening it up to the study of the deep forces, rooted in society, that shape international life, to the study of the interactions between domestic political life and foreign policy, and so on; but also the new research directions explored since then, whether in terms of broadening the deep force-field to economy, mentalities and culture, or widening the point of view from the national to the multilateral to the transnational.

To highlight the various problematic axes, the seminar will progress along thematic lines, and we will tackle each of these axes - reading reports, occasional illustrative subjects, the study of documents of various kinds...

Some bibliographical references:

ARON Raymond. Paix et guerre entre les nations. Paris, Calmann-Lévy, 1984.

FRANK Robert dir. Pour l’histoire des relations internationales. Paris, PUF, 2012.

KISSINGER Henry. Diplomatie. Paris, Fayard, 1996.

RENOUVIN Pierre, DUROSELLE Jean-Baptiste. Introduction à l’histoire des relations internationales. Paris, Colin, 1991.

SOUTOU Georges-Henri. La guerre de cinquante ans. Paris, Fayard, 2001.

This seminar aims to provide students with a legal culture, enabling them to discover the problems faced by managers of public and private companies.
Thanks to this seminar, students should be better able to perceive the consequences of legal factors in the economic, social and financial life of the company.

Criminal liability of executives and managers in the business world.

Bibliography

Jean-Paul Antona and François Lenglart. Introduction au droit de l'entreprise. Éditions Dalloz. 1997.

Level required: No prerequisites, other than sufficient ease in French.

Evaluation: Attendance and participation. One-hour written test at the end of the last session.