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# Events for 01/29/2021 from all calendars

## Seminar in Random Tensors

## Noncommutative Geometry Seminar

## Mathematical Physics and Harmonic Analysis Seminar

## Algebra and Combinatorics Seminar

**Time: ** 11:00AM - 12:00PM

**Location: ** zoom

**Speaker: **Grigoris Paouris, TAMU

**Title: ***Canceled*

**Time: ** 1:00PM - 2:00PM

**Location: ** Zoom 951 5490 42

**Speaker: **Pierre Albin, University of Illinois at Urbana-Champaign

**Title: ***The sub-Riemannian limit of a contact manifold*

**Abstract: **Contact manifolds, which arise naturally in mechanics, dynamics, and geometry, carry natural Riemannian and sub-Riemannian structures and it was shown by Gromov that the latter can be obtained as a limit of the former. Subsequently, Rumin found a complex of differential forms reflecting the contact structure that computes the singular cohomology of the manifold. He used this complex to describe the behavior of the spectra of the Riemannian Hodge Laplacians in the sub-Riemannian limit. As many of the eigenvalues diverge, a refined analysis is necessary to determine the behavior of global spectral invariants. I will report on joint work with Hadrian Quan in which we determine the global behavior of the spectrum by explaining the structure of the heat kernel along this limit in a uniform way.

**URL: ***Event link*

**Time: ** 2:00PM - 2:50PM

**Location: ** Zoom

**Speaker: **Chris Marx, Oberlin College

**Title: ***Potential dependence of the density of states: deterministic, ergodic, and random potentials*

**Abstract: **In this talk we will address the potential dependence of the density of states and related spectral functions for discrete Schr\"odinger operators on infinite graphs. Following ideas by J. Bourgain and A. Klein, we will consider the density of states {\em{outer}} measure (DOSoM), a {\em{deterministic}} quantity, which is well defined for {\em{all}} Schr\"odinger operators.
We will explicitly quantify the potential dependence of the DOSoM in weak topology by proving a modulus of continuity with respect to the potential in $\ell{l}^\infinity$-norm. The resulting modulus of continuity reflects the geometry of the graph at infinity. For the special case of operators on $\mathbb{Z}^d$ our result implies Lipschitz continuity of the DOSoM, in the case of the Bethe lattice, we obtain that the DOSoM is $\frac{1}{2}$-log-H\"older continuous. Applications of this result to ergodic, and in further consequence, for random Schr\"odinger operators will be presented.
This talk is based on joint work with Peter Hislop (University of Kentucky).

**Time: ** 3:00PM - 4:00PM

**Location: ** Zoom

**Speaker: **Eric Rowell, TAMU

**Title: ***Representations of Braid Groups and Motion Groups*

**Abstract: **Representations of braid groups appear in many (related) guises, as sources of knot and link invariants, transfer matrices in statistical mechanics, quantum gates in topological quantum computers and commutativity morphisms in braided fusion categories. Regarded as trajectories of points in the plane, the natural generalization of braid groups are groups of motions of links in 3 manifolds. While much of the representation theory of braid groups and motions groups remains mysterious, we are starting to see hints that suggest a few conjectures. I will describe a few of these conjectures and some of the progress towards verification.