Department of

Mathematics


Seminar Calendar
for events the day of Wednesday, October 3, 2018.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Wednesday, October 3, 2018

1:00 pm in 2 Illini Hall,Wednesday, October 3, 2018

Dynamics and Spectral Theory 2: Hearing the length spectrum

Hadrian Quan

Abstract: In this talk, we’ll introduce the wave kernel, and demonstrate how an analysis of its singularities can (sometimes!) determine the lengths of closed geodesics on compact manifolds. We’ll focus on surfaces, and study the relation between geodesic length rigidity and Laplace spectral rigidity. This will necessarily involve some results for pseudodifferential operators, however this will be presented alongside a “user’s guide” to pseudodifferential operators.

3:00 pm in 241 Altgeld Hall,Wednesday, October 3, 2018

Measurable matchings and Følner tilings: Part 1

Anush Tserunyan (UIUC Math)

Abstract: We read through "Følner tilings of actions of amenable groups" by C. Conley et al [arXiv]. This first talk will introduce to amenable groups and actions, and analyze Hall's marriage theorem for locally finite bipartite graphs (which involves an ultrafilter or the Axiom of Choice). More importantly, we will discuss an example of a closed graphs on $[0,1]$, which satisfies Hall's condition, hence admits a perfect matching, yet not a measurable one.

4:00 pm in 245 Altgeld Hall,Wednesday, October 3, 2018

Connecting the upper half plane, geodesic flows, and continued fractions

Claire Merriman (UIUC Math)

Abstract: Continued fractions are frequently studied in number theory, but they can also be described geometrically. I will talk about continued fraction expansions as dynamical systems, and connect this symbolic system to tessellations. The first part will focus on the "regular" or "simple" continued fractions, where all of the numerators are 1. Then, I will show what happens when all of the numerators are $\pm 1$ and the denominators are all even or all odd.

4:00 pm in 2 Illini Hall,Wednesday, October 3, 2018

Flops and derived categories of threefolds, Part 1

Sungwoo Nam (UIUC Math)

Abstract: In his paper, Bridgeland showed that derived categories of threefolds, which are related by flopping operations, are equivalent. Besides its own interest, this result can be used to study behavior of invariants of threefolds under birational morphisms. In this talk, we will present Bridgeland's work for two weeks. As the main idea involves constructing flop as a moduli space of perverse point sheaves, I'll introduce some notions such as derived categories and t-structures and their properties relevant to the proof. After that, I will give application of the theorem on birational Calabi-Yau threefolds and curve counting invariants.