Graduate Geometry and Topology Seminar
- Event Type
- Seminar/Symposium
- Sponsor
- Department of Mathematics
- Location
- Altgeld Hall 347
- Date
- Mar 1, 2024 4:00 - 4:50 pm
- Speaker
- Anthony D’Arienzo
- Cost
- n/a
- Contact
- Anthony D’Arienzo
- apd6@illinois.edu
- Views
- 50
Title: Hodge theory and Cohomology
Abstract: Hodge theory is bridge between the topological properties of a smooth manifold, its cohomology, and its analytical properties, namely harmonic forms. This bridge enables the study of spaces whose topology break down yet still have a sensible notion of a smooth function space. I will review the classical example of this bridge: showing that every cohomology class on a smooth manifold has a unique harmonic form. Afterwards I will highlight some examples where this bridge can study generalized our singular spaces.