MGSC Website: http://math.uci.edu/~mgsc/
As one of the deepest and most beautiful theorems in geometry, the Hodge theorem builds a bridge between Riemannian metric and topological invariants. It gives an isomorphism between the space of harmonic p forms on a Riemannian manifold and the p de Rham cohomology group of a smooth structure. By the de Rham theorem, we see the isomorphism between the space of harmonic p forms and p real singular cohomology group.
The Hodge theorem is a good example of how PDEs help us understand geometric structure and even topological structure. In this talk, we will give an introduction to this theorem, explain the idea behind it, and give some applications in Riemannian geometry.
Lihan loves running for long time, just running, even without music. She also enojys swimming in the early morning and seeing the sun coming out.
Peter Li is currently Lihan's advisor.
none
Pizza will be served after the talk.