Department of

Mathematics


Seminar Calendar
for events the day of Monday, October 14, 2019.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, October 14, 2019

3:00 pm in 441 Altgeld Hall,Monday, October 14, 2019

Motivating Higher Toposes: Higher Bundle Theory

Joseph Rennie (UIUC Math)

Abstract: In this (self-contained) talk, I will begin with a quick recap of the motivation for higher bundle theory from the first talk. I will then say a few words about Toposes, and proceed to spend the majority of the talk attempting to develop a general theory of higher bundles. Along the way, we will see how the necessary properties for this development (almost) force higher topos structure. (Technical details will be sacrificed for intuitive clarity. No particular model of higher categories will be imposed.)

3:00 pm in 243 Altgeld Hall,Monday, October 14, 2019

Supersymmetric localization and the Witten genus

Dan Berwick-Evans (Illinois)

Abstract: Equivariant localization arguments generalize the Duistermaat–Heckman formula, allowing one to express an integral on a manifold in terms of integrals over fixed point sets of a torus action. Supersymmetric localization seeks to apply these formulas to path integrals in quantum field theory. In fortuitous cases, this affords a rigorous definition of the path integral. I will explain one such example in a 2-dimensional quantum field theory built on a classical theory of maps from elliptic curves to a smooth manifold. Up to a certain choice of orientation (which may be obstructed), the path integral is well-defined. The volume of the mapping space (i.e., the path integral of 1) turns out to be the Witten genus, an invariant of smooth manifolds valued in modular forms.

5:00 pm in 241 Altgeld Hall,Monday, October 14, 2019

The Dixmier Trace

Haojian Li (UIUC)

Abstract: We will construct so-called exotic traces on the space of bounded operators on a Hilbert space, the so called Dixmier traces. In the long run we are interested in geometric applications of Connes' Dixmier trace calculus.