Department of

# Mathematics

Seminar Calendar
for events the day of Friday, April 14, 2017.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, April 14, 2017

3:00 pm in 141 Altgeld Hall,Friday, April 14, 2017

#### Some applications of the BV-BFV formalism on manifolds with boundary

###### Alberto Cattaneo (University of Zurich)

Abstract: According to Segal and Atiyah, a quantum field theory on manifolds with boundary should be thought of as, roughly speaking, the assignment of a vector space (space of states) to the boundary and an element thereof (the state or the evolution operator) to the bulk, in a way that is compatible with gluing. In this talk (based on joint work with P. Mnev and N. Reshetikhin) I will describe how this has to be reformulated when working in perturbation theory. In particular, I will discuss the perturbative quantization of gauge theories on manifolds with boundary. It turns out that, under suitable assumptions, the bulk symmetries, treated in the BV formalism, naturally give rise to a cohomological description of the reduced phase space (BFV formalism) in a correlated way that can be quantized.

4:00 pm in 345 Altgeld Hall,Friday, April 14, 2017

#### Baire measurable colorings of group actions: Part Ⅱ

###### Anton Bernshteyn (UIUC Math)

Abstract: Suppose that a countable group $\Gamma$ acts continuously on a Polish space $X$ and denote this action by $\alpha$. Does there exist a Baire measurable coloring $f \colon X \to \mathbb{N}$ satisfying certain local constraints? Or, better to say, can we characterize the coloring problems which admit Baire measurable solutions over $\alpha$? We will show that, on the one hand, there is no such Borel characterization—the problem is complete analytic. On the other hand, when $\alpha$ is the shift action, we prove that, roughly speaking, a Baire measurable coloring exists if and only if it can be found by a greedy algorithm.

4:00 pm in 241 Altgeld Hall,Friday, April 14, 2017

#### Net and Filter Convergence Spaces

###### Chris Gartland (UIUC Math)

Abstract: A net or filter convergence space is a set together with a collection of data that axiomatizes the notion of convergence to an element of that set. In this sense, convergence spaces generalize topological spaces. More specifically, we will define the (equivalent) categories of net and filter convergence spaces and show that they contain the category of topological spaces (Top) as a full subcategory. We'll highlight some of the advantages these categories have over Top, especially in relation to Tychonoff's theorem. This talk is based off a series of blog posts by Jean Goubault-Larrecq, http://projects.lsv.ens-cachan.fr/topology/?page_id=785.