## Seminar

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## Interactions between symplectic geometry, combinatorics and number theory (14722.0105)

## "Rigidity of Vector bundles"

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## Mo. 14-15.30

## Stefan Cohn-Vossen Raum des Mathematischen Instituts (Raum 313)

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The seminar Interactions between symplectic geometry, combinatorics and number theory will cover different topics, and is aimed at studying the interactions among them. In particular, we will learn about genera on complex or symplectic manifolds (for instance the Todd and Hirzebruch genus and elliptic genera) and their connections with modular forms, as well as the combinatorics of lattice polytopes, in particular Ehrhart theory and reflexive polytopes.

In this semester we will study vector bundles which are rigid, namely their equivariant index is indeed a constant. In particular we will go over the paper by R. Bott and C. Taubes entitled "On the rigidity theorems of Witten", where a beautiful proof of the rigidity of the elliptic genera of spin manifolds is given.

Graduate students, postdocs and professors interested in attending will be encouraged to give explanatory talks that are suitable to an audience with diverse background.

From time to time we will also invite external speakers to give more advanced/research talks on topics related to the relevant themes of the seminar (but not necessarily on rigidity of vector bundles).

15.04.2019: Silvia Sabatini, "An introduction to rigid vector bundles"

29.04.2019: Isabelle Charton, "On the fixed point formula for elliptic complexes"

06.05.2019: Alexander Caviedes Castro, "Elliptic operators, signature and loop spaces"

13.05.2019: Stéphanie Cupit-Foutou (Bochum), "On the Gromov-width of Kähler compact multiplicity-free manifolds"

20.05.2019: Michael Wiemeler (Münster), "A bordism theoretic proof of the rigidity of elliptic genera"

27.05.2019: Panagiotis Konstantis (Philipps-Universität Marburg), "The diffeomorphism type of GKM 6-manifolds and an application to Hamiltonian non-Kähler actions"

03.06.2019: Alexander Caviedes Castro, "Elliptic operators, signature and loop spaces, Part II"