Abstract: The main purpose of this talk is to introduce to the audiences about one of the keystones in the theory of elliptic operators and serves as a starting point of Hodge theory, say, Hodge decomposition theorem. Rather than stressing on complicated proofs, I would like to give a series of fundamental materials that are essential for the proof of the theorem as well as its corollaries such as Poincaré duality and Serre duality. A concrete example I shall present is the Fubini-Study metrics on the projective spaces which are related to the original idea of Hodge in his paper "The Theory and Applications of Harmonic Integrals". A short introduction to Hodge conjecture will also be provided.

Time: 17h30, Thursday, September 3, 2020.

Online via Zoom

https://us04web.zoom.us/j/74914721760?pwd=L1VOOGEwVHZTb2htejBjUzd6aDlsdz09