Un of Tenn | Math Department

Seminars and Colloquiums
for the week of February 8, 2010

Speaker:

Professor Jim Conant, Monday
Dr. Cory Hauck, ORNL, Monday
Prof. Jolanta Misiewicz, Warsaw Technical University, Monday
Professor Vasileios Maroulas, Institute for Mathematics and its Applications, University of Minnesota, Tuesday
Mr. Chad Kilpatrick, Wednesday
Dr. Ziga Virk, Friday
Professor Jian Song, University of Kansas, Friday

Monday, February 8

TOPOLOGY SEMINAR
TIME: 11:15 – 12:05 p.m.
ROOM: EST 209
SPEAKER: Professor Jim Conant
TITLE: “Khovanov Homology II”
ABSTRACT: In this talk, we will discuss Khovanov's fascinating generalization of the Jones polynomial. This theory assigns a combinatorially defined chain complex to every link diagram, in such a way that the homology of this chain complex is a link invariant. Moreover, the graded Euler characteristic is nothing other than the Jones polynomial. I will try to make this talk accessible to newcomers.

Computational & Applied Math/DE Seminar
TIME: 3:35 p.m.
ROOM: HBB 112
SPEAKER: Dr. Cory Hauck, ORNL
TITLE: “A numerical regularization technique for multi-scale, linear transport models”
ABSTRACT: We present a regularization technique for the PN -equations: a linear hyperbolic system of PDEs that is commonly used to model particle transport through a material medium. In collision-dominated regimes, the PN -equations have a well-known asymptotic limit that is described by a standard diffusion equation. However, this limit is difficult to capture with conventional hyperbolic solvers that are based on the upwind methodology, due to (i) excessive numerical dissipation and (ii) a stiff CFL condition. The regularization technique, which is derived by splitting the PN -system into fast and slow dynamics, does capture the proper diffusion limit and provides a useful tool for multi-scale problems with regions of both high and low collisionality. We present initial results for some one-dimensional test problems and discuss areas for continued development.

PROBABILITY SEMINAR
TIME: 3:35 - 4:25 p.m.
ROOM: HBB 132
SPEAKER: Prof. Jolanta Misiewicz, Warsaw Technical University
TITLE: “Levy-Khintchine representation for generalized convolutions”
ABSTRACT: The idea of generalized convolutions was introduced by Kingman and Urbanik. In this talk, we study infinitely divisible distributions with respect to such convolutions and present an analog of the Levy-Khintchine representation. We give the corresponding analog of Gaussian and compound Poisson measures for weak generalized convolutions.

Tuesday, February 9

COLLOQUIUM
TIME: 3:35 – 4:25 p.m.
ROOM: HBB 102
SPEAKER: Professor Vasileios Maroulas, Institute for Mathematics and its Applications, University of Minnesota
TITLE: “Multi-object Bayesian filtering”
ABSTRACT: Tracking simultaneously a large collection of targets is a challenging problem with great interest in several disciplines such as engineering, biology, ecology, etc. In this talk, we address the problem of dynamically estimating multiple objects within a Bayesian filtering framework. Modeling a plethora of individual targets as a set-valued state and adopting the random set theory as a unified approach to multi-target tracking result in the propagation of a multi-target Bayesian filtering distribution. Furthermore, we will examine and implement two moments of the multi-target filtering distribution, the probability hypothesis density (PHD) and the cardinalized PHD respectively. This is a joint work with Ron Mahler.

Wednesday, February 10

COURSE GEOMETRY SEMINAR
TIME: 11:15 – 12:05 p.m.
ROOM: EST 209
SPEAKER: Mr. Chad Kilpatrick
TITLE: “Property A is Equivalent to Nuclearity and Exactness for Countable Discrete Groups G”
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.

Friday, February 12

TOPOLOGY SEMINAR
TIME: 11:15 – 12:05 p.m.
ROOM: EST 209
SPEAKER: Dr. Ziga Virk
TITLE: “Homotopical smallness and closeness”
ABSTRACT: We present the notions of homotopical smallness and closeness, discuss their role in homotopy theory and present some examples.

COLLOQUIUM
TIME: 3:35 – 4:25 p.m.
ROOM: HBB 102
SPEAKER: Professor Jian Song, University of Kansas
TITLE: “Fractional martingales and characterization of the fractional Brownian motion”
ABSTRACT: We introduce the notion of fractional martingale as the fractional derivative of order alpha of a continuous local martingale, where alpha is in (-1/2,1/2), and we show that it has a nonzero finite variation of order 2/(1+2 alpha), under some integrability assumptions on the quadratic variation of the local martingale. As an application we establish an extension of Levy's characterization theorem for the fractional Brownian motion.

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.

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