# Events for 10/25/2019 from all calendars

## Austin-TAMU Probability and Related Fields

**Time: ** 09:30AM - 5:00PM

**Location: ** Bloc 506A

**Description: **Austin-TAMU Probability and Related Fields: Fall 2019

The Austin-TAMU probability and Related Fields day is a twice-yearly event, alternately held at UT Austin and Texas A&M. Our fifth-ever meeting will be held at TAMU on Friday, October 25th, 2019 in the Blocker Building (room TBD) with four speakers, an open problem session, and plenty of time for discussion and collaboration. See the schedule for more details about the schedule.

All talks (including coffee and lunch) will take place in RLM. From 10am-2pm we will be in room 8.136. From 2pm-4pm we will be in room 10.176.

For those visiting from Austin, TAMU will reimburse you for gas and parking costs. Please try to car pool for both the environment and to cut costs.
Deadline:
Please register by October 11th.
Speakers:
Boris Hanin (TAMU)
Hanbaek Lyu (UCLA)

**URL: ***Event link*

## Probability Seminar

**Time: ** 11:30AM - 12:30PM

**Location: ** BLOC 628

**Speaker: ** Hanbaek Lyu, UCLA

**Title: ***TBA*

**Abstract: **TBA

## Postdoc Lunch Time Talks

**Time: ** 12:00PM - 12:20PM

**Location: ** BLOC 220

**Speaker: **Bob Booth, Texas A&M University

**Description: **

Title: Some Existence Results for Nonlinear Wave EquationsAbstract:We will discuss long-time and global existence results for nonlinear wave equations with small initial data. High dimensional solutions enjoy an improvement in their life-span compared to the three-dimensional case, where one can only obtain `almost global existence' (as opposed to global existence). We will review prior results, including works of Klainerman, John-Klainerman, Keel-Smith-Sogge, and Metcalfe-Sogge. If time permits, we will discuss classes of non-trapping, asymptotically Euclidean wave operators which can be large perturbations of the typical D'Alembertian operator.

## Postdoc Lunch Time Talks

**Time: ** 12:35PM - 12:55PM

**Location: ** BLOC 220

**Speaker: **Shuang Ming, Texas A&M University

**Description: **

Title: Quantum representations of braid groups and mapping class groupsAbstract:The Kauffman's bracket used for computing Jones polynomial of a link give us a way to make resolutions to crossings. Naturally, Kauffman's bracket defines a set of projective representations of braid groups. These representations turns out to be hom-spaces of certain modular tensor categories. Thus, these constructions generalize to representations of mapping class groups of surfaces with or without boundary. In a project with Greg Kuperberg, we study the irreducibility and denseness of these representations. In today's talk, I will talk about the idea of our proof with the very beginning example.

## Postdoc Lunch Time Talks

**Time: ** 12:55PM - 1:15PM

**Location: ** BLOC 220

**Speaker: **Diane Guignard, Texas A&M University

**Description: **

Title: "Numerical Approximations of Prestrained Plates"Abstract:"We study the elastic behaviour of prestrained plates. When actuated, the plates deform out of plane to reduce their internal stresses. The mathematical model consists of the minimization of a bending energy under the constraint that the first fundamental form of the deformed plate satisfies a given metric. In this talk, I will give a brief description of the model and the proposed numerical scheme. The performance of the later will be illustrated through several numerical experiments."

## Mathematical Physics and Harmonic Analysis Seminar

**Time: ** 1:50PM - 2:50PM

**Location: ** BLOC 628

**Speaker: **P. Kuchment, TAMU

**Title: ***On generic non-degeneracy of spectral edges. Discrete case*

**Abstract: **This is joint work with Frank Sottile (TAMU) and Ngoc T. Do (Missouri State U.)

An old problem in mathematical physics deals with the structure of the dispersion relation of the Schrodinger operator -Delta+V(x) in R^n with periodic potential near the edges of the spectrum, i.e. near extrema of the dispersion relation. A well known and widely believed conjecture says that generically (with respect to perturbations of the periodic potential) the extrema are attained by a single branch of the dispersion relation, are isolated, and have non-degenerate Hessian (i.e., dispersion relations are graphs of Morse functions). In particular, the important notion of effective masses hinges upon this property.

The progress in proving this conjecture has been slow. It is natural to try to look at discrete problems, where the dispersion relation is (in appropriate coordinates) an algebraic, rather than analytic, variety. Moreover, such models are often used for computation in solid state physics (the tight binding model). Alas, counterexamples showing that the genericity can fail in some discrete situations do exist.

In our work, we consider the case of a general periodic discrete operator depending polynomially on some parameters. We prove that the non-degeneracy of extrema either fails or holds for all but a proper algebraic subset of values of parameters. Thus, a random choice of a point in the parameter space will give the correct answer "with probability one". A specific example of a diatomic Z^2-periodic structure is also considered, which provides a cornucopia of examples for both alternatives, as well as a different approach to the genericity problem.

## Student/Postdoc Working Geometry Seminar

**Time: ** 2:00PM - 3:00PM

**Location: ** BLOC 624

**Speaker: **JM Landsberg, TAMU

**Title: ***2nn and 3nn matrix multiplication*

## Algebra and Combinatorics Seminar

**Time: ** 3:00PM - 3:50PM

**Location: ** BLOC 506A **

**Speaker: **Frank Sottile, Texas A&M University

**Title: ***Composed Schubert Problems*

**Abstract: **A composition of Schubert problems is a construction that takes two Schubert problems on possibly different Grassmannians and gives a Schubert problem on a larger Grassmannian whose number of solutions is the product of the numbers of solutions of the original problems. This generalizes a construction that was discovered while classifying Schubert problems with imprimitive Galois groups.

I will explain this construction and the product formula, which has both an algebraic and a bijective proof. I will also discuss how this construction is related to Galois groups of Schubert problems. This is joint work with Li Ying and Robert Williams.

## Student Working Seminar in Groups and Dynamics

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

**Location: ** BLOC 605AX

**Speaker: **Konrad Wrobel

**Title: ***Furstenberg Correspondence and Szemeredi's Theorem*

**Abstract: **I will present a very rough outline of Furstenberg's proof of Szemeredi's theorem. In doing so, I plan to translate the problem into a problem in ergodic theory and outline the classification of measure preserving systems due to Furstenberg and Zimmer.

## Linear Analysis Seminar

**Time: ** 4:00PM - 5:00PM

**Location: ** BLOC 628 **

**Speaker: **Jordyn Harriger, Indiana University

**Title: ***Planar Algebras Related to the Symmetric Groups*

**Abstract: **THIS IS A JOINT SEMINAR WITH GEOMETRY, ALGEBRA & COMBINATORICS

**URL: ***Event link*

## Geometry Seminar

**Time: ** 4:00PM - 5:00PM

**Location: ** BLOC 628

**Speaker: **Jordyn Harriger, Indiana University

**Title: ***Planar Algebras Related to the Symmetric Groups.*

**Abstract: **What makes the symmetric groups special ? Well, one interesting thing about
S_n is that it has a subgroup of index n and that the permutation representation
of S_n comes from inducing the trivial representation of that subgroup. How
could this generalize if n was not an integer? Using planar algebras we can
describe Rep(S_n) graphically. Then using this graphical description we can
construct a planar algebra for Rep(S_t), where t is not an integer, via inter-
polation between the Rep(S_n)'s. Additionally, I will describe how this planar
algebra can from a special biadjunction between tensor categories, which gen-
eralizes the induction and restriction relations between S_n and S_{n-1}. I will
also discuss the relationship between these planar algebras and usual partition
algebra description of Rep(S_t).