- Hodge theory and exotic geometries
- Since Poincaré, the mathematical properties of topological spaces have been studied by associating algebraic invariants with them.
When the topological space is provided with a suitable metric, it is possible to use analysis to represent these algebraic invariants as solutions of a Laplace equation on the geometric space in question. This is the subject of a mathematical theory named after the Scottish mathematician William Hodge.
What happens when the geometric structure degenerates and space becomes singular? A central question with multiple links to physics by its nature.
- Teaching coordinator: Amini Omid