Speaker:	Simone Hu (Oxford University)
Title:	Cocycles for GLn, graph complexes and Feynman integrals
Date (JST):	Wed, Sep 30, 2026, 13:30 - 15:00
Place:	Seminar Room B
Abstract:	In this talk we will describe a program that explores connections between the cohomology of the general linear group,  graph complexes, and Feynman integrals via invariant differential forms. In particular, we study families of closed differential forms defined on the space of positive definite symmetric matrices that are invariant under the action of GLn(Z) up to a sign. These "orientation forms" give rise to infinitely many new classes in the unstable cohomology of GLn(Z) and, via the tropical Torelli map, they can be used to define cocycles for Kontsevich's odd graph complex. Finally, we establish a connection to TQFTs, where the simplest example of an orientation form arises in integrals computing quantum corrections. This is based on joint work with Francis Brown and Erik Panzer, with Paul-Hermann Balduf, and work in-progress.

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