Department of

# Mathematics

Seminar Calendar
for events the day of Friday, November 22, 2019.

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events for the
events containing

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, November 22, 2019

2:00 pm in 347 Altgeld Hall,Friday, November 22, 2019

#### A category interpolating Yetter-Drinfeld modules over symmetric groups

###### Robert Laugwitz (University of Nottingham)

Abstract: P. Deligne introduced a remarkable tensor category Rep(St) interpolating the representation theory of symmetric groups, allowing for the natural number of permuted letters to be replaced by any complex number t. This category is defined using diagrams. We compute objects in the monoidal center of this category to obtain a ribbon category that interpolates the category of Yetter-Drinfeld modules over symmetric groups. As an application, interpolations of untwisted Dijkgraaf-Witten invariants. These are polynomial invariants of framed links. I will motivate Deligne's category Rep(St) and the monoidal center construction before describing how objects of the center or Rep(St) are obtained. This talk is based on joint work with Johannes Flake, RWTH Aachen University.

3:00 pm in 341 Altgeld Hall,Friday, November 22, 2019

#### Eigenvalues in Euclidean and Hyperbolic Geometry

###### Xiaolong Hans (UIUC Math)

Abstract: In this talk, we will explore the beauty and power of eigenvalues Laplacian operator. We start by talking about basic properties of Laplacian, Rayleigh quotient, monotonicity, how the lowest eigenvalues detect the difference of a geometric object from being a ball, Cheeger's inequality and how it distinguishes two different classes of infinite volume hyperbolic manifolds. The talk will emphasize intuition with no background in Laplacian assumed.

5:00 pm in 241 Altgeld Hall,Friday, November 22, 2019

#### Stochastic Differential Equations and Unitaries (Part 3)

###### Marius Junge (UIUC)

Abstract: Applications of Brownian motion and SDE. For example, show that an operator is completely positive by using SDE.