# Next Week's Events

## Seminars

Click on seminar heading to go to seminar page.

• ### Algebra Seminar

Monday September 25, 2017 at 13:30, Wachman Hall, Rm. 617
Introduction to Categories, III

Vasily Dolgushev, Temple University

I will talk about limits and colimits of functors. I will present various examples including profinite completions of groups. If time will permit, I will start talking about monoidal categories and monoidal functors.

• ### Analysis Seminar

Monday September 25, 2017 at 14:40, Wachman 617

Luis Fernando Ragognette, Federal University of São Carlos, Brazil

The goal of this talk is to present results on infinite order differential operators and its applications to local solvability of a differential complex associated to a locally integrable structure in a Gevrey environment.

One of the reasons why infinite order differential operators are important in this setting is a structural theorem that says that every ultradistribution of order $s$ can be locally represented by an infinite order differential operator applied to a Gevrey function of order $s$, this new kind of representation is crucial in several applications that we are going to discuss.

• ### Colloquium

Monday September 25, 2017 at 16:00, Wachman 617
Left-orderability and 3-manifold groups

Cameron Gordon, University of Texas at Austin

The fundamental group is a more or less complete invariant of a 3-dimensional manifold. We will discuss how the purely algebraic question of whether or not this group has a left-invariant total order appears to be related to two other, seemingly quite different, properties of the manifold, one geometric and the other essentially analytic.

• ### Probability Seminar

Tuesday September 26, 2017 at 16:00, UPenn (David Rittenhouse Lab 4C8)
Cutoff for random to random

Evita Nestoridi, Princeton

Random to random is a card shuffling model that was created to study strong stationary times. Although the mixing time of random to random has been known to be of order n log n since 2002, cutoff had been an open question for many years, and a strong stationary time giving the correct order for the mixing time is still not known. In joint work with Megan Bernstein, we use the eigenvalues of the random to random card shuffling to prove a sharp upper bound for the total variation mixing time. Combined with the lower bound due to Subag, we prove that this walk exhibits cutoff at $\frac{3}{4} n log n$, answering a conjecture of Diaconis.

• ### Global Analysis Seminar

Wednesday September 27, 2017 at 11:40, Wachman 527

Max Reinhold Jahnke, University of São Paulo, Brazil

We are going to continue our discussion about Lie algebra cohomology and its relation to classic cohomology theories. We are going to discuss a result by Chevalley and Eilenberg on the De Rham cohomology of compact Lie groups, its relation to Bott's theorem and how to combine them to study certain left-invariant elliptic involutive structures on semisimple compact Lie groups.

• ### Geometry and Topology Seminar

Wednesday September 27, 2017 at 14:45, Wachman 617
Free products and diffeomorphisms of compact manifolds

Thomas Koberda, University of Virginia

Abstract: It is a well-known fact that if $G$ and $H$ are groups of homeomorphisms of the interval or of the circle, then the free product $G*H$ is also a group of homeomorphisms of the interval or of the circle, respectively. I will discuss higher regularity of group actions, showing that if $G$ and $H$ are groups of $C^{\infty}$ diffeomorphisms of the interval or of the circle, then $G*H$ may fail to act by even $C^2$ diffeomorphisms on any compact one-manifold. As a corollary, we can classify the right-angled Artin groups which admit faithful $C^2$ actions on the circle, and recover a joint result with H. Baik and S. Kim. This is joint work with S. Kim.

• ### Applied Mathematics and Scientific Computing Seminar

Wednesday September 27, 2017 at 16:00, 617 Wachman Hall

Peter Benner, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg

Friday September 29, 2017 at 13:00, Wachman 617
Representations from roots of the Alexander polynomial

Timothy Morris, Temple University