Seminars and Colloquia by Series

A note on Olsen inequality

Series
Analysis Seminar
Time
Wednesday, November 26, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Yoshihiro Sawano – Gakushuin University, Japan

Please Note: Note time change.

Let I_\alpha be the fractional integral operator. The Olsen inequality, useful in certain PDEs, concerns multiplication operators and fractional integrals in the L^p-norm, or more generally, the Morrey norm. We strenghten this inequality from the one given by Olsen.

A Constructive Characterization of the Split Closure of a Mixed Integer Linear Program

Series
ACO Student Seminar
Time
Wednesday, November 26, 2008 - 13:30 for 2 hours
Location
ISyE Executive Classroom
Speaker
Juan Pablo Vielma – ISyE, Georgia Tech
Two independent proofs of the polyhedrality of the split closure of Mixed Integer Linear Program have been previously presented. Unfortunately neither of these proofs is constructive. In this paper, we present a constructive version of this proof. We also show that split cuts dominate a family of inequalities introduced by Koppe and Weismantel.

High-order numerical methods for nonlinear PDEs

Series
PDE Seminar
Time
Tuesday, November 25, 2008 - 15:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Bojan Popov – Texas A&M University

In this talk we will consider three different numerical methods for solving nonlinear PDEs:

  1. A class of Godunov-type second order schemes for nonlinear conservation laws, starting from the Nessyahu-Tadmor scheme;
  2. A class of L1 -based minimization methods for solving linear transport equations and stationary Hamilton- Jacobi equations;
  3. Entropy-viscosity methods for nonlinear conservation laws.

All of the above methods are based on high-order approximations of the corresponding nonlinear PDE and respect a weak form of an entropy condition. Theoretical results and numerical examples for the performance of each of the three methods will be presented.

Dunkl processes, eigenvalues of random matrices and the Weyl-chamber

Series
Stochastics Seminar
Time
Tuesday, November 25, 2008 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Nizar Demni – University of Bielefeld
We will introduce the Dunkl derivative as well as the Dunkl process and some of its properties. We will treat its radial part called the radial Dunkl process and light the connection to the eigenvalues of some matrix valued processes and to the so called Brownian motions in Weyl chambers. Some open problems will be discussed at the end.

Astala's conjecture on Hausdorff measure distortion under planar quasiconformal mappings

Series
Analysis Seminar
Time
Monday, November 24, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Ignacio Uriarte-tuero – Michigan State University
In his celebrated paper on area distortion under planar quasiconformal mappings (Acta 1994), K. Astala proved that a compact set E of Hausdorff dimension d is mapped under a K-quasiconformal map f to a set fE of Hausdorff dimension at most d' = \frac{2Kd}{2+(K-1)d}, and he proved that this result is sharp. He conjectured (Question 4.4) that if the Hausdorff measure \mathcal{H}^d (E)=0, then \mathcal{H}^{d'} (fE)=0. This conjecture was known to be true if d'=0 (obvious), d'=2 (Ahlfors), and more recently d'=1 (Astala, Clop, Mateu, Orobitg and UT, Duke 2008.) The approach in the last mentioned paper does not generalize to other dimensions. Astala's conjecture was shown to be sharp (if it was true) in the class of all Hausdorff gauge functions in work of UT (IMRN, 2008). Finally, we (Lacey, Sawyer and UT) jointly proved completely Astala's conjecture in all dimensions. The ingredients of the proof come from Astala's original approach, geometric measure theory, and some new weighted norm inequalities for Calderon-Zygmund singular integral operators which cannot be deduced from the classical Muckenhoupt A_p theory. These results are intimately related to (not yet fully understood) removability problems for various classes of quasiregular maps. The talk will be self-contained.

On Cannon's conjecture

Series
Geometry Topology Seminar
Time
Monday, November 24, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Sa'ar Hersonsky – University of Georgia
Cannon: "A f.g. negatively curved group with boundary homeomorphic to the round two sphere is Kleinian". We shall outline a combinatorial (complex analysis motivated) approach to this interesting conjecture (following Cannon, Cannon-Floyd-Parry). If time allows we will hint on another approach (Bonk-Kleiner) (as well as ours). The talk should be accessible to graduate students with solid background in: complex analysis, group theory and basic topology.

On the formation of adiabatic shear bands

Series
PDE Seminar
Time
Friday, November 21, 2008 - 16:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Athanasios Tzavaras – Univeristy of Maryland
We consider a system of hyperbolic-parabolic equations describing the material instability mechanism associated to the formation of shear bands at high strain-rate plastic deformations of metals. Systematic numerical runs are performed that shed light on the behavior of this system on various parameter regimes. We consider then the case of adiabatic shearing and derive a quantitative criterion for the onset of instability: Using ideas from the theory of relaxation systems we derive equations that describe the effective behavior of the system. The effective equation turns out to be a forward-backward parabolic equation regularized by fourth order term (joint work with Th. Katsaounis and Th. Baxevanis, Univ. of Crete).

Vizing's Independence Number Conjecture on Edge Chromatic Critical Graphs

Series
Combinatorics Seminar
Time
Friday, November 21, 2008 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Nick Zhao – University of Central Florida
In 1968, Vizing proposed the following conjecture which claims that if G is an edge chromatic critical graph with n vertices, then the independence number of G is at most n/2. In this talk, we will talk about this conjecture and the progress towards this conjecture.

Multiple knots in a manifold with the same surgeries yielding S^3

Series
Geometry Topology Seminar
Time
Friday, November 21, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Ken Baker – University of Miami
Lickorish observed a simple way to make two knots in S^3 that produced the same manifold by the same surgery. Many have extended this result with the most dramatic being Osoinach's method (and Teragaito's adaptation) of creating infinitely many distinct knots in S^3 with the same surgery yielding the same manifold. We will turn this line of inquiry around and examine relationships within such families of corresponding knots in the resulting surgered manifold.

Smoothed Weighted Empirical Likelihood Ratio Confidence Intervals for Quantiles

Series
Stochastics Seminar
Time
Thursday, November 20, 2008 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Jian-Jian Ren – Department of Mathematics, University of Central Florida
So far, likelihood-based interval estimate for quantiles has not been studied in literature for interval censored Case 2 data and partly interval-censored data, and in this context the use of smoothing has not been considered for any type of censored data. This article constructs smoothed weighted empirical likelihood ratio confidence intervals (WELRCI) for quantiles in a unified framework for various types of censored data, including right censored data, doubly censored data, interval censored data and partly interval-censored data. The 4th-order expansion of the weighted empirical log-likelihood ratio is derived, and the 'theoretical' coverage accuracy equation for the proposed WELRCI is established, which generally guarantees at least the 'first-order' accuracy. In particular for right censored data, we show that the coverage accuracy is at least O(n^{-1/2}), and our simulation studies show that in comparison with empirical likelihood-based methods, the smoothing used in WELRCI generally gives a shorter confidence interval with comparable coverage accuracy. For interval censored data, it is interesting to find that with an adjusted rate n^{-1/3}, the weighted empirical log-likelihood ratio has an asymptotic distribution completely different from that by the empirical likelihood approach, and the resulting WELRCI perform favorably in available comparison simulation studies.

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