Un of Tenn | Math Department

Seminars and Colloquiums
for the week of March 1, 2010

Speaker:

Professor Jie Xiong, Monday
Professor Stella Huerfano, Monday
Professor Joan Lind, Belmont University, Monday
Mr. Chad Kilpatric, Wednesday
Mr. Zachary Smith, Wednesday
Professor Jerzy Dydak, Friday
Professor Xiaoming Wang, Florida State University, Friday

Monday, March 1

PROBABILITY SEMINAR
TIME: 10:10 – 11:00 a.m.
ROOM: AC 113
SPEAKER: Professor Jie Xiong
TITLE: “Large deviation principle for diffusion processes under a nonlinear expectation”
ABSTRACT: Motivated from the study of mathematical finance, we establish a large deviation principle of the Freidlin-Wentzell type under nonlinear probability for diffusion processes with a small diffusion coefficient. We extend and provide a new proof for a variational identity of Bou\'e and Dupuis which is widely used in deriving the large deviation principle under classical linear probability. Navier-Stokes equation plays an important role in our deriving the large deviation result.

TOPOLOGY SEMINAR
TIME: 11:15 – 12:05 p.m.
ROOM: Temple 303
SPEAKER: Professor Stella Huerfano
TITLE: "Frobenius Extensions in relation to TQFT's and Khovanov Type Homologies: an overview"
ABSTRACT: The concepts of Frobenius extension and Frobenius system will be introduced. After reviewing the definition of a TQFT (Topological Quantum Field Theory), some examples of Homologies of Khovanov type will be given for certain Frobenius systems.

COLLOQUIUM
TIME: 3:35 – 4:25 p.m.
ROOM: HBB 102
SPEAKER: Professor Joan Lind, Belmont University
TITLE: “Geometry of Loewner Evolution”
ABSTRACT: When Oded Schramm introduced Schramm-Loewner Evolution (or SLE) in 2000, he was working to answer questions about 2-dimensional random walks, and he utilized the Loewner differential equation. This equation, a classical tool in complex analysis, provides a one-to-one correspondence between continuous real-valued functions (called driving functions) and certain families of growing sets in the upper halfplane (called hulls.) For $\kappa >0$, the process SLE($\kappa$) can be thought of as the family of hulls that correspond to the random driving term $\sqrt{\kappa} B_t$, where $B_t$ is Brownian motion. As $\kappa$ increases, the geometry of the hulls changes, with two phase transitions: from simple curves to self-intersecting curves at $\kappa=4$, and to spacefilling curves at $\kappa=8$. The geometry of these curves are of independent interest, and we will discuss their H\"older continuity.

In the deterministic setting, less is known about the relationship between the geometry of the hulls and properties of the driving functions. We will look at several examples of ``bad" geometric behavior (such as fractal curves, spacefilling curves, or spirals) that correspond to ``nice" driving functions. Additionally, we will discuss the two phase transitions for deterministic functions, which are analogous to the two phase transitions for SLE. Some of this work is joint work with Don Marshall and Steffen Rohde.

Wednesday, March 3

COARSE GEOMETRY SEMINAR
TIME: 11:15 – 12:05 p.m.
ROOM: Temple 303
SPEAKER: Mr. Chad Kilpatrick
TITLE: “Property A is Equivalent to Nuclearity and Exactness for Countable
Discrete Groups G” III
ABSTRACT: In this talk, we will see that for a countable discrete group G, property A is equivalent to:
1.    Cr*(G) is exact
2.    Cu*(G) is nuclear
3.    Cu*(G) is exact.
Here, a C*-algebra A is defined to be nuclear if for any finite subset F of A, the identity map may be approximated on F by unital completely positive maps which factorize through Mn(C), for some n. In this talk, I closely follow Ch. 4: "Connections with C*-Algebras” from Rufus Willet’s Some Notes on Property A.

ANALYSIS SEMINAR
TIME: 3:35-4:30
ROOM: HBB 132
SPEAKER: Mr. Zachary Smith
TITLE: von Neumann type inequalities and a commutant lifting theorem, 2

Friday, March 5

TOPOLOGY SEMINAR
TIME: 11:15 – 12:05 p.m.
ROOM: Temple 303
SPEAKER: Professor Jerzy Dydak
TITLE: “Introduction to CAT(0) spaces IV”

COLLOQUIUM
TIME: 3:35 – 4:35 p.m.
ROOM: HBB 102
SPEAKER: Professor Xiaoming Wang, Florida State University
TITLE: “Approximating long time statistical properties of large chaotic systems”
ABSTRACT: It is well-known that physical laws for many large chaotic dynamical systems arising in fluid dynamics are revealed statistically. We present recent progress as well as existing challenges on how to approximate these long time statistical properties for a few fluid problems.

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. Steve Wise.

Week of: