Seminars and Colloquiums
for the week of March 4, 2013
Speakers:
Prof. Paul Jung, University of Alabama, Birmingham, Monday
Prof. Luis Finotti, Monday
Mr. Keith Penrod, Tuesday
Prof. Remus Nicoara, Wednesday
Mr. Eric Numfor, Wednesday
Dr. Jeffrey Hankins, Thursday
Prof. Elton Hsu, Northwestern, Friday
*** Tea Time this week will be Monday - Wednesday at 3:00 pm.
Hosted this week by John Cummings, Jennifer Ribbeck, and Jillian Trask. Everyone is welcome! ***
MONDAY, MARCH 4
PROBABILITY SEMINAR
TIME: 3:35 - 4:25
ROOM: Ayres 122
SPEAKER: Prof. Paul Jung, University of Alabama, Birmingham
TITLE: "Random walks at random times"
ABSTRACT: Kesten and Spitzer (1979) introduced random walks in random scenery (RWRS) which are collective reward processes where a random walker collects a random reward (or scenery) at each site it visits. If the walker visits a site N times, it collects the same reward N times thus leading to correlations in the collective reward process. Cohen and Samorodnitsky (2006) studied a certain renormalization of RWRS and proposed self-similar, symmetric alpha-stable processes, which generalize fractional Brownian motion, as their scaling limits. The limiting processes have self-similarity exponents H>1/alpha.
We consider a modification of RWRS in which a sign associated to the reward (scenery) alternates upon successive visits of the random walk. The resulting process is what we call a random walk at random time, and it generalizes the so-called iterated random walk. We will discuss renormalizations of this discrete process, and in particular, show that the alternating scenery can lead to limiting processes which have self-similarity exponents H<1/alpha.
ALGEBRA SEMINAR
TIME: 3:35 - 4:25
ROOM: Ayres B004
SPEAKER: Prof. Luis Finotti
TITLE: "On the ABC Conjecture, part III"
ABSTRACT: S. Mochizuki has recently claimed to have prove the ABC Conjecture. This is a very strong conjecture, with numerous consequences in number theory. If correct, it would be the most important result in mathematics since the proof of the Poincaré Conjecture. In this series of talks we will motivate, state, give equivalent statements, prove/discuss consequences and study related problems to the ABC Conjecture. (We will not give Mochizuki's "proof", which is extremely technical and advanced.)
TUESDAY, MARCH 5
DOCTORAL DEFENSE
TIME: 2:10 p.m.
ROOM: Buehler 472
SPEAKER: Mr. Keith Penrod
TITLE: "Big Homotopy Groups"
His committee consists of Professors Dydak (chair), Brodskiy, Conant, Thistlethwaite,
and Gerloff (Ag Econ).
WEDNESDAY, MARCH 6
ANALYSIS SEMINAR
TIME: 3:35 - 4:25
ROOM: Ayres 114
SPEAKER: Prof. Remus Nicoara
TITLE: "Non-conjugate actions of groups on von Newmann algebras"
ABSTRACT: We will first review some known results about groups acting on von Newmann algebras. We will then construct certain parametric classes of non-conjugate actions on the hyperfinite II_1 factor.
MATH BIOLOGY SEMINAR
TIME: 3:35 - 4:25
ROOM: Ayres 405
SPEAKER: Eric Numfor
TITLE: Nonlinear Dynamics in Physiology and Medicine (Chapter 2 of this book)
THURSDAY, MARCH 7
TOPOLOGY SEMINAR
TIME: 9:40 - 10:55
ROOM: Ayres B004
SPEAKER: Dr. Jeffrey Hankins
TITLE: "A Uniform Box Product Primer"
ABSTRACT: In Jocelyn Bell's thesis, she constructed a space which she proved was normal, countably paracompact, and collectionwise Hausdorff. However, she left open a few questions about the uniform box product. The speaker will address and definitively answer a subset of these questions, such as whether her space is collectionwise normal or paracompact, and introduce a collection of such spaces of interest to set-theoretic topologists.
FRIDAY, MARCH 8
COLLOQUIUM
TIME: 3:35 - 4:25
ROOM: Ayres 405
SPEAKER: Prof. Elton Hsu, Northwestern University
TITLE: Stochastic Analysis on Riemannian Manifolds
ABSTRACT: The fundamental solution of the heat equation on a Riemannian manifold associated with the Laplace-Beltrami operator can be served as the transition density function of a stochastic process called Brownian motion on the manifold. Many geometric properties of the manifold are reflected in the random behavior of Brownian motion. In this talk I will discuss several such results, in which stochastic techniques are used to prove results of purely geometric nature. On the other hand, Brownian motion on a Riemannian manifold can be regarded as a measure on the path space over the Riemannian manifold, a good example of infinite dimensional Hilbert manifold. This point of view gives rise to functional analysis on the path space. We will use this point of view to discuss logarithmic Sobolev, transportation cost, and other functional inequalities on the path space. The talk is oriented towards general audience with a liberal education in classical and geometric analysis.
Snacks will be available at 3:00 p.m.
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:
Seminars from 2011-2012 academic year
Seminars from 2010-2011 academic year
Seminars from 2009-2010 academic year
Seminars from 2008-2009 academic year
Seminars from 2007-2008 academic year
Seminars from 2006-2007 academic year