Cohomology in algebra, geometry, physicsand statistics

The Topological Half of the Grothendieck-Hirzebruch-Riemann-Roch Theorem

Speaker’s name:

Eugenio Landi

Speaker’s affiliation:

Pennsylvania State University

Place:

ZOOM meeting

Date:

Wednesday, 9. November 2022 - 13:30 to 14:30

Abstract:

The HRR theorem famously states that the holomorphic Euler characteristic of X with coefficients in a holomorphic vector bundle V equals $\int_X ch(V)td(X)$. This can be rewritten as two theorems: the first one, analytical, identifying $\chi(X,V)$ with the K-theoretic pushforward of V to the point, while the second, purely topological, identifying the pushforward with the integral. The same can be said for the GHRR theorem and pushforwards along proper holomorphic maps between holomorphic manifolds. I will focus on the second half, introducing orientations and pushforwards in cohomology and explaining how the presence of the Todd class is natural and expected.

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We shall open the seminar room+ZOOM meeting at 13.15 for coffee

Join Zoom Meeting

https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09

MeetingID:99598413922

Passcode:Galois

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We shall open the seminar room+ZOOM meeting at 13.15 for coffee

Join Zoom Meeting

https://cesnet.zoom.us/j/99598413922?pwd=YXNFbk50aVhleXhWSGtISFViLytRUT09

MeetingID:99598413922

Passcode:Galois