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Luis Fernando Ragognette, University of São Paulo, 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.
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.
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.
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.
Peter Benner, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg
Timothy Morris, Temple University
There are no conferences next week.