Un of Tenn | Math Department

Seminars and Colloquiums
for 2010-2011

Week of February 28, 2011

Speaker:
Mr. Fei Xing, Monday
Ms. Sarah White, Tuesday
Professor James Conant, Tuesday
Professor Ohannes Karakashiann, Wednesday
Professor Carl Sundberg, Wednesday
Dr. Dror Bar-Natan, Toronto, Friday

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 Dr. Fernando Schwartz.

Monday, February 28

PROBABILITY SEMINAR
TIME: 3:35 – 4:25 p.m.
ROOM: Ayres 114
SPEAKER: Mr. Fei Xing
TITLE: “Almost sure asymptotics for random motion of Poisson potential”
ABSTRACT: Consider a particle doing a random movement in R^d space. Independent of the particle, there are some random obstacles located in the space. The particle will gain energy from the obstacles during the movement. The classical way of modeling this phenomenon is to consider a Brownian motion in homogeneous Poisson environment. An interesting question of this model is to study the almost surely (w.r.t. environment) long time asymptotic for the exponential moment of the energy obtained by the Brownian particle. It turns out that this exponential moment has many applications, for instance, it is the solution of the parabolic Anderson model, it is the normalized constant for the random Gibbs measure, etc.

I am interested in the interaction between the random motion and the random environment and I explore the relation by computing the long time asymptotic for the exponential moment under different combinations. In my talk, I will first introduce the background and list some existing results on this topic and then present some questions I am interested in as well as the result I obtained by exploring this topic.

Tuesday, March 1

MATH BIOLOGY SEMINAR
TIME: 9:45 – 10:35 a.m.
ROOM: NIMBioS Classroom
SPEAKER: Sarah White
TOPIC: Continuous-Time Birth and Death Chains, part I

TOPOLOGY SEMINAR
TIME: 3:40 p.m. – 4:30 p.m.
ROOM: Ayres Hall 406
SPEAKER: Prof. James Conant
TITLE: “Whitney concordance and a conjecture of Levine”
ABSTRACT: (Joint with Rob Schneiderman and Peter Teichner) We describe a refinement of link concordance called Whitney concordance. This is defined similarly to concordance, except that the annuli are allowed to have certain types of singularities. We show how Milnor invariants almost classify this relation, but that a sequence of higher order Arf invariants, whose existence is currently unknown, is needed to complete the classification. One of the main ingredients is a combinatorial conjecture of Levine, relating an abelian group of unrooted trees with a certain group coming from the free (quasi) Lie algebra. We recently proved Levine’s conjecture, and we will give some hints about how the proof goes.

Wednesday, March 2

APPLIED/COMPUTATIONAL MATH
TIME: 3:35 - 4:30 p.m.
ROOM: Ayres 111
SPEAKER: Professor Ohannes Karakashian
TITLE: “Adaptive Methods for Elliptic PDEs”, Part IV

ANALYSIS SEMINAR
TIME: 3:35 - 4:25 p.m.
ROOM: Ayres 114
SPEAKER: Professor Carl Sundberg
TOPIC: “The Dirac - Kadison/Singer – Paving – Feichtinger – Seip – Sundberg Conjectures”
ABSTRACT: I’m not kidding about this. The same type of question has arisen in many different areas, such as Quantum Mechanics, C*-Algebra Theory, Frame Theory, and Function-Theoretic Operator Theory (notice that I have shamelessly added my own name to this list). I will discuss these questions and their interrelations.

Friday, March 4

MATHEMATICS COLLOQUIUM
TIME: 3:35 – 4:25 p.m.
ROOM: Ayres 405
SPEAKER: Dr. Dror Bar-Natan, Toronto
TITLE: “Cosmic Coincidences and Several Other Stories”
ABSTRACT: In the first half of my talk I will tell a cute and simple story - how given a knot in R3 one may count all possible "cosmic coincidences" associated with that knot, and how this count, appropriately packaged, becomes an invariant Z with values in some space A of linear combinations of certain trivalent graphs. In the second half of my talk I will describe (rather sketchily, I'm afraid) a part of the story surrounding Z and A: How the same Z also comes from quantum field theory, Feynman diagrams, and configuration space integrals. How A is a space of universal formulas which make sense in every metrized Lie algebra and how specific choices for that Lie algebra correspond to various famed knot invariants. How Z solves a universal topological problem, and how solving for Z is solving some universal Lie-algebraic problem. All together, this is the u-story.

In the remaining time I will mention several other Z's and A's and the parallel (yet sometimes interwoven) stories surrounding them - the v-story, and w-story, and perhaps also the p-story. Each of these stories is clearly still missing some chapters.

For more on this talk please see: http://www.math.toronto.edu/~drorbn/Talks/Tennessee

Refreshments available in Ayres 401 at 3:15 p.m.

Past notices:

winter break