Department of

Mathematics


Seminar Calendar
for events the day of Friday, March 4, 2016.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, March 4, 2016

2:00 pm in 445 Altgeld Hall,Friday, March 4, 2016

Quasiconformal Maps in the Grushin Plane

Matthew Romney (UIUC Math)

Abstract: First, we provide a survey of the modern theory of quasiconformal maps in increasingly general metric space settings. Second, we will discuss the specific case of quasiconformal maps in the Grushin plane, an important example of a sub-Riemannian manifold. This is based on work with C. Gartland and D. Jung.

2:00 pm in 447 Altgeld Hall,Friday, March 4, 2016

Scattering-symplectic geometry

Melinda Lanius (UIUC)

Abstract: We will introduce scattering-symplectic manifolds, manifolds equipped with a type of minimally degenerate Poisson structure that is not too restrictive so as to have a large class of examples, yet restrictive enough for standard Poisson invariants to be computable. We will define this geometry, give examples, and discuss the Poisson cohomology.

4:00 pm in 241 Altgeld Hall,Friday, March 4, 2016

The Topological Hochschild Homology of $\mathbb{Z}$

Juan Villeta-Garcia (UIUC Math)

Abstract: In the 1980's Bökstedt introduced Topological Hochschild Homology (THH), as a variant of algebraic Hochschild Homology, where tensoring over a ground ring was replaced by smashing over the sphere spectrum. Even for discrete rings, like the integers $\mathbb{Z}$, this construction provided new invariants. Bökstedt shortly thereafter calculated the THH of $\mathbb{Z}$ and $\mathbb{Z}/p\mathbb{Z}$, by exploiting heavy topological methods. Algebraically, though, a crucial tool was a spectral sequence relating classical Hochschild Homology to THH. In this talk we will introduce the spectral sequence, and sketch out a proof. We will then hint at a method of Brun to generalize to higher quotients, $\mathbb{Z}/p^n\mathbb{Z}$.

4:00 pm in 345 Altgeld Hall,Friday, March 4, 2016

An analogue of Cobham's theorem for graph directed iterated function systems

Philipp Hieronymi (UIUC)

Abstract: We read the paper "An analogue of Cobham's theorem for graph directed iterated function systems" by Charlier, Leroy and Rigo (Advances in Mathematics 280 (2015) 86–120).