Department of

# Mathematics

Seminar Calendar
for events the day of Monday, November 18, 2019.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, November 18, 2019

3:00 pm in 441 Altgeld Hall,Monday, November 18, 2019

#### Splitting induced from transfer

###### Abhra Abir Kundu (UIUC Math)

Abstract: Associated to a finite covering map is a map in homology and cohomology, known as transfer, which goes in the opposite direction. This map usually doesn’t come from a map at the level of spaces but interestingly enough it does when we look at its version in spectra. This often leads to interesting splittings in spectra after appropriate localisation. In this talk, I will explain how one gets this map. Then I will concentrate on one such transfer and the splitting induced from it. I will show a few pictures of algebraic objects associated to this transfer which will illustrate this splitting and then end by observing some facts about the splitting from those pictures.

3:00 pm in 243 Altgeld Hall,Monday, November 18, 2019

#### Local symplectic groupoids, their generating functions and quantization

###### Alejandro Cabrera (Universidade Federal do Rio de Janeiro)

Abstract: We will first review how Poisson brackets can be seen as the infinitesimal data underlying certain types of transformations which form a 'local symplectic groupoid'. The composition map in this structure defines a lagrangian submanifold and this, in turn, can be locally described by a generating function. We show how to obtain an explicit analytic formula for this generating function for any Poisson bracket on a coordinate space and how this formula reproduces, upon suitable Taylor expansion, a certain tree-level part of a formula given by Kontsevich in the context of quantization. We will also discuss further the link between the generating function, symplectic realizations, and general quantizations, as well as their connection to a related 2d field theory (the 'Poisson-sigma model'). The first part of this talk is based on joint work with B. Dherin.

5:00 pm in 241 Altgeld Hall,Monday, November 18, 2019

#### Graph Hormanders

###### Marius Junge (University of Illinois at Urbana-Champaign)

Abstract: I would talk about the link between graph Laplacians and Hormander systems of orthogonal groups.