Tue, 18 Feb 2025
15:30
L4

Invariance of elliptic genus under wall-crossing

Henry Liu
(IPMU Tokyo)
Abstract

Elliptic genus, and its various generalizations, is one of the simplest numerical invariants of a scheme that one can consider in elliptic cohomology. I will present a topological condition which implies that elliptic genus is invariant under wall-crossing. It is related to Krichever-Höhn’s elliptic rigidity. Many applications are possible: to GIT quotients, moduli of sheaves, Donaldson-Thomas invariants, etc.

Wed, 15 Jan 2020

14:00 - 15:00
L3

Curve counting via stable objects in derived categories of Calabi-Yau 4-folds

Yalong Cao
(IPMU Tokyo)
Further Information

In a joint work with Davesh Maulik and Yukinobu Toda, we proposed a conjectural Gopakumar-Vafa type formula for the generating series of stable pair invariants on Calabi-Yau 4-folds. In this talk, I will present the recent joint work with Yukinobu Toda on how to give an interpretation of the above GV type formula in terms of wall-crossing phenomena in the derived category of coherent sheaves. 

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