Department of

# Mathematics

Seminar Calendar
for events the day of Monday, October 22, 2018.

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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, October 22, 2018

3:00 pm in 241 Altgeld Hall,Monday, October 22, 2018

#### Measurable matchings and Følner tilings: Part 4

###### Ruiyuan (Ronnie) Chen (UIUC Math)

Abstract: We read through "Følner tilings of actions of amenable groups" by C. Conley et al [arXiv]. In this fourth and hopefully last talk, we will sketch the proof of the Banach density version of the Rokhlin lemma.

3:00 pm in 345 Altgeld Hall,Monday, October 22, 2018

#### Power operations in complex $K$-theory

###### William Balderrama (UIUC Math)

Abstract: The complex $K$-theory of a finite-dimensional space $X$ is a ring that can be defined in terms of the structure of complex vector bundles over $X$. Certain operations on vector bundles, such as taking exterior powers, enrich the $K$-theory of $X$ with further structure, and this extra structure has historically added to the applicability of complex $K$-theory. In this talk, I will explain how these operations can be obtained from certain equivariant refinements of the $n$'th tensor power operations, relating these operations to the representation theory of symmetric groups.

4:00 pm in 245 Altgeld Hall,Monday, October 22, 2018

#### Random Tilings: Pathways to Arctic Phenomena

###### Phillippe DiFrancesco   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: The problem of tiling some finite domain of the plane with finitely many types of tiles can often be rephrased as that of enumeration of configurations of non-intersecting lattice paths with fixed ends. For large scaled domains, random tilings may exhibit a sharp separation between "frozen" regions tiled regularly i.e. exhibiting a crystalline structure, and "liquid" regions with disordered tiling. This is the so-called arctic phenomenon. After reviewing techniques for enumerating paths, we present a new method for deriving arctic curves based on the path interpretation of large random tilings.

5:00 pm in 241 Altgeld Hall,Monday, October 22, 2018

#### On Talagrand's deviation inequality for product measures, II

Abstract: We follow Ledoux's approach to deviation inequalities.