Department of

# Mathematics

Seminar Calendar
for Symplectic and Poisson Geometry Seminar events the year of Tuesday, March 13, 2018.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
    February 2018            March 2018             April 2018
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Monday, February 5, 2018

3:00 pm in 243 Altgeld Hall,Monday, February 5, 2018

#### Symplectic groupoids of cluster Poisson structures

###### Songhao Li (University of Notre Dame)

Abstract: Cluster algebras appears as the coordinate ring of many interesting objects. We recall the notion of a cluster ensemble which consists of a cluster A variety and its corresponding cluster X variety. The compatible Poisson structures on these spaces are log-canonical. We construct the symplectic groupoid of the log-canonical Poisson structure on each cluster chart, and lift the cluster mutations to groupoid mutations.

Monday, February 19, 2018

3:00 pm in 243 Altgeld Hall,Monday, February 19, 2018

#### Symplectic groupoids and monoidal Fukaya categories

###### James Pascaleff (UIUC)

Abstract: I will describe how a groupoid structure on a symplectic manifold naturally induces a monoidal structure on its Fukaya category. This provides a unifying perspective on the various known monoidal structures on Fukaya categories. As an application, I will use this framework to address the question of when Lagrangian Floer cohomology rings are commutative.

Monday, March 12, 2018

3:00 pm in 243 Altgeld Hall,Monday, March 12, 2018

#### Morse theory and a stack of broken lines

###### Hiro Tanaka (Harvard)

Abstract: I'll talk about a stack encoding the moduli space of gradient trajectories on a point (which is, I promise, less trivial than it sounds). It turns out that Morse theory on any manifold defines a sheaf on this stack, and that this sheaf in turn allows us to encode Morse theory as a deformation problem. I'll touch on the generalization to Floer theory, too. These constructions conjecturally allow one to construct Floer theory and Morse theory with coefficients in spectra when appropriate obstructions vanish. This is joint work with Jacob Lurie.

Monday, March 26, 2018

3:00 pm in 243 Altgeld Hall,Monday, March 26, 2018

#### Integration of Structure Equations of G-Structures

###### Ivan Struchiner (University of Sao Paulo)

Abstract: The infinitesimal data attached to a (finite type) class of G-structures with connections are its structure equations. Such structure equations give rise to Lie algebroids endowed with extra geometric information. On the other hand, given such a Lie G-algebroid a natural question is that of the existence of a G-structure with connection which corresponds to the given G-algebroid through differentiation. This integration problem is called Cartan's Realization Problem for G-structures. In this talk I will describe a way of solving the realization problem by integrating the G-algebroid. I will focus on the case of Riemannian metrics (G=O(n)). The talk is based on joint work with Rui Loja Fernandes.

Monday, April 16, 2018

3:00 pm in 243 Altgeld Hall,Monday, April 16, 2018

#### The globalization of the Poisson sigma model in the BV-BFV formalism

###### Nima Moshayedi (University of Zurich)

Abstract: One of the central problems of mathematical physics is understanding how to pass from classical to quantum physics. One procedure that implements that passage, called deformation quantization, achieves quantization by deforming the Poisson algebra of classical observables into a non-commutative algebra of quantum observables. The algebraic structure of the quantum observables is determined by the star product, which is a formal deformation of the algebraic structure on the classical observables. Kontsevich showed that any Poisson manifold admits a star product and gave an explicit formula for it. The Poisson Sigma Model (PSM) is an AKSZ-theory closely related to deformation quantization. We will give a short introduction to the BV-BFV formalism, the PSM and discuss briefly how we can construct a globalized version of Kontsevich's star product using this formalism by extending a condition called the modi fied Quantum Master Equation to a differential version of it.

Monday, April 30, 2018

3:00 pm in 243 Altgeld Hall,Monday, April 30, 2018

#### Ice cream geometry: a mathematical activity and coloring book

###### Melinda Lanius (UIUC)

Abstract: Have you ever wondered how computers do geometry? Come find out! We'll color a souped-up color-by-numbers to develop a general notion of circle and ball. Sketch some curves in geodesic connect-the-dots to see what happens when straight lines bend. Meander through `metric' mazes to appreciate the wonky ways of non-homogenous spaces. Feel free to bring pens and pencils in a wide variety of colors. They'll come in handy!