# Research Recruitment Seminar

This is a seminar in which faculty advertise their research areas to prospective graduate students.

Early program graduate students are especially encouraged to attend, but anyone is welcome.

To sign up to speak in this seminar, please fill out this form.

This seminar is organized by Lorenzo Najt and Yu Sun, please contact them with questions.

**Spring 2018**

In general the time of this seminar is flexible (though we will try to stick to 4PM on Mondays and 12 Noon on Fridays), so please check each talk for the exact time and location.

Time: 12-1 on Friday, Feb 9th 2018

Location: B215

Speaker: Jean-Luc Thiffeault

Title: **Applied topology, mixing, and microswimmers**

Abstract: "I will discuss several topics of my current research, which involves applications of topology and partial differential equations. First, we'll see how ideas from braids and mapping class groups can be used to investigate the behavior of dynamical systems as well as characterize braiding of actual textiles. Nest, we'll examine how the mixing of fluids can be studied via PDEs, and some connections to probability theory. Finally, I'll discuss probabilistic problems for swimming microorganisms, such as dispersion and consumption of resources."

Time: 4-5 on Monday, Feb 12 2018

Location: B115 in Van Vleck

Speaker: Paul Terwilliger

Title: **Tridiagonal pairs and applications**

Abstract: A tridiagonal pair is a linear algebraic object that appears in many subjects, such as (i) Combinatorics (Q-polynomial graphs); (ii) Lie theory (sl2, affine sl2, tetrahedron algebra); (iii) Quantum groups (Uqsl2, affine Uqsl2, q-tetrahedron algebra); (iv) Physics (Onsager algebra, q-Onsager algebra); (v) Special functions (q-Racah polynomials etc from the Askey scheme of orthogonal polynomials); (vi) Representation theory (the universal Askey-Wilson algebra, DAHA of type (C1V, C1).

We will describe some main facts about tridiagonal pairs, and discuss some of the above connections. The talk is nontechnical and meant for a wide audience.

Time: 12 on Friday, Feb 16 2018

Location: B215

Speaker: Daniel Erman

Title: **Syzygies**

Abstract: I’ll discuss some of the subtleties that arise when one tries to do linear algebra over the polynomial ring, as well as connections to algebraic geometry.

Time: 4-5 on Monday, Feb 19 2018

Location: B115

Speaker: Saverio Spagnolie

Title: **Fluid-structure interactions, from biolocomotion and active suspensions to liquid crystals**

Abstract: I will discuss a few problems in the interactions of simple/complex fluids and immersed deformable structures, ranging from the evolution of locomotion on the planet to the dynamics and self-assembly of soft, active matter. I will show how the development of novel numerical techniques can be used alongside classical methods of applied mathematics to study the coupled nonlinear PDEs that describe these exciting physical systems, and point to a number of open problems in these fields.

Time: 12 on Friday, Feb 23 2018

Location: B215

Speaker: Sigurd Angenent

Title: **Curve shortening in the plane and in space.**

Abstract: Curve shortening is one of the simplest geometric evolution equations like Mean Curvature Flow, Ricci Flow, Yang-Mills flow, harmonic map flow, Willmore flow. I’ll talk about what is known (a lot) and what isn’t known (much more) about singularities in curve shortening for plane curves and for space curves.

Time: Tuesday, March 20, 4pm

Location: B139

Speaker: Betsy Stovall

Title: **Two endpoint bounds via inverse problems**

Abstract: In Mathematics in general, and Analysis in particular, one strategy for solving a problem is to begin by understanding what a counter-example would look like. In this talk, we will apply a quantitative version of this approach to prove two endpoint results, one for a Fourier Restriction operator and one for an averaging operator. The latter is joint work with Christ, Dendrinos, and Street.