**Seminars and Colloquiums**

for the week of April 3, 2017

for the week of April 3, 2017

*SPEAKER:*

Jeremy Siegert, UTK, Monday

Mark Bly, UTK, Monday

Vy Nguyen, UTK, Tuesday

Israel Michael Sigal, University of Toronto, Tuesday

Huy Tran, UCLA, Wednesday

Phuc Nguyen, Louisiana State University, Thursday

Dietmar Bisch, Vanderbilt University, Friday

*TEA TIME -
3:00 pm – 3:30 pm
Monday - Wednesday: Ayres 401
*

*Hosted by: Cameron Cook & Jack Ryan*

**Monday, April 3rd**

TOPOLOGY/GEOMETRY SEMINAR

TITLE: Topics in coarse geometry: Higson corona

SPEAKER: Jeremy Siegert, UTK

TIME: 2:30p – 3:20p

ROOM: 113 Ayres

Abstract: TBA

ALGEBRA SEMINAR

TITLE: Finite Fields, Subspaces, and Inversions

SPEAKER: Mark Bly, UTK

TIME: 3:35p – 4:25p

ROOM: 113 Ayres

In the combinatorics community, a connection between Vector Subspace Chains of a finite field, Direct Sum Decompositions of a finite field, and inversions in sequences of integers is fairly widely known. For example, here at UTK, this connection is explored in a 500-level combinatorics course sequence. That said, an explicit enumeration of the connection between these objects is not very widely known. In the talk, we will discuss this less well-known explicit enumeration.

**Tuesday, April 4th**

STOCHASTICS/ PROBABILITY SEMINAR

TITLE: Local time and Excursions of Markov Process

SPEAKER: Vy Nguyen, UTK

TIME: 2:10p - 3:25p

ROOM: 113 Ayres

The purpose of this presentation is to investigate the structure of the successive lengths of intervals of excursion of a Markov process X away from a point. To this end, we will first discuss the Poisson processes and subordinators. Then, we construct an increasing process L, called the local time, which stays constant on the excursion intervals. The right continuous inverse of L is a subordinator whose jumps correspond to the lengths of the excursion intervals. The study culminates with the description of the process of the excursions of X in terms of a Poisson point process.

DIFFERENTIAL EQUATIONS SEMINAR

TITLE: Blowup Dynamics in the Keller-Segel Model of Chemotaxis.

SPEAKER: Israel Michael Sigal, University of Toronto

TIME: 3:40p – 4:40p

ROOM: 113 Ayres

The Keller-Segel equations model chemotaxis of bio-organisms. In a reduced form, considered in this talk, they are related to Vlasov equation for self-gravitating systems and are used in social sciences in descriptions of crime patterns.

It is relatively easy to show that in the critical dimension 2 and for the mass of initial conditions greater than 8 \pi, the solutions break down in finite time. Understanding the mechanism of this breakdown turned out to be a subtle problem defying solution for a long time.

Preliminary results indicate that the solutions 'blowup'. This blowup is supposed to describe the chemotactic aggregation of the organisms and understanding its universal features would allow comparison of theoretical results with experimental observations.

In this talk I discuss recent results on dynamics of solutions of the (reduced) Keller-Segel equations in the critical dimension 2, which include a formal derivation and partial rigorous results on the blowup dynamics of solutions. The talk is based on joint work with S. I. Dejak, D. Egli and P.M. Lushnikov.

**Wednesday, April 5th **

ANALYSIS SEMINAR

TITLE: Loewner equations from a complex dynamic point of view

SPEAKER: Huy Tran, UCLA

TIME: 2:30p – 3:20p

ROOM: 113 Ayres

The Loewner equation gives a one-to-one correspondence between growing slit curves in a domain and certain real-valued continuous functions, which are called driving, functions. This is a tool created by Loewner to solve the Bieberbach conjecture. Later, Schramm used it to study conformally invariant measures of curves arisen from statistical physics and probability by letting the driving functions be multiples of one-dimensional Brownian motion.

In the talk, we will give a background on (Schramm-) Loewner equation. Then we will give an interesting connection to holomorphic motion, a concept in complex dynamics. One of the keys is to consider driving functions, which are complex-valued.

**Thursday, April 6th **

DIFFERENTIAL EQUATIONS SEMINAR

TITLE: Local energy bounds and $\epsilon$-regularity criteria for the 3D Navier-Stokes system

SPEAKER: Phuc Nguyen, Louisiana State University

TIME: 2:10p – 3:10p

ROOM: 113 Ayres

The system of three-dimensional Navier-Stokes equations is considered. We obtain some new local energy bounds that enable us to improve several $\epsilon$-regularity criteria. The key idea here is to view the head pressure as a signed distribution belonging to certain fractional Sobolev space of negative order. This allows us to capture the oscillation of the pressure in our criteria.

The talk is based on joint work with Cristi Guevara.

**Friday, April 7th **

SPEICAL COLLOQUIUM

TITLE: Subfactors with infinite representation theory

SPEAKER: Dietmar Bisch, Vanderbilt University

TIME: 2:30p – 3:30p

ROOM: 405 Ayres

Since the discovery of the Jones polynomial in the 1980's, it is well known that sub factors of von Neumann factors are intimately related to quantum topology. A subfactor is said to have infinite representation theory, if its standard representation generates infinitely many non-equivalent irreducibles. Such subfactors are hard to construct, and very few methods are known to produce interesting examples. I will highlight one such procedure, due to Jones and myself. The construction yields new C$^*$-tensor categories and solutions of the quantum Yang-Baxter equation. I will try to make the talk accessible to non-experts

*If you are interested in giving or arranging a talk for one of our seminars or colloquiums, please review our calendar. *

*If you have questions, or a date you would like to confirm, please contact colloquium AT math DOT utk DOT edu *

**Past notices:**

3/13/17 - Spring Break

Winter Break