Weekly Calendar

January 16 - January 19, 2001

Monday Tuesday Wednesday Thursday Friday

Seminars Announcements Conferences Calendar Archive

Items for inclusion in the Weekly Calendar can now be submitted using the new submission form. Other questions or comments related to the Weekly Calendar should be sent to Hilda Britt. Deadline for inclusion in the Weekly Calendar is noon every Wednesday. Speakers are encouraged to provide abstracts.

Orange & Blue Bar

TUESDAY, JANUARY 16

2 Illini Hall, 11:00 a.m.
PROBABILITY AND STATISTICS SEMINAR
Professor Jeff Douglas, Departments of Biostatistics and Medical Informatics, University of Wisconsin-Madison
Item response models for joint analysis of quality of life and survival in clinical trials
Abstract: A complication when assessing quality of life data longitudinally is that in many clinical trials a substantial percentage of patients die before completing all of the assessments. Furthermore, a patient's risk of dying might be predicted by his current quality of life. This suggests jointly modeling quality of life and survival, and using this combined information to summarize the outcome. The aim of this research is to address complicated issues, such as death, present in analyzing multiple-item ordinal quality of life data in clinical trials while recognizing the psychometric properties of the quality of life instrument being used. This is accomplished by combining item response models and Cox's proportional hazard model with time-dependent covariates, where a latent variable process for quality of life determines the probability of selecting various options on quality of life items, and also serves as a time-dependent covariate in the survival model. We accomplish this using Markov chain Monte Carlo methods to obtain parameter estimates. Then we compute a summary measure, area-under-QOL-curve, to compare the efficacy of the treatments. The methods are illustrated with analysis of data from the Vesnarinone Trial of patients with severe heart failure, in which quality of life was assessed with the Minnesota Living with Heart Failure Questionnaire.

P.S.: If you are interested in meeting Professor Douglas, please contact Usha Dhar at u-dhar.edu or 244-7192 to set up a time.

314 Altgeld Hall, 2:00 p.m.
SPECIAL SEMINAR
Kevin M. Pilgrim, Department of Mathematics and Statistics, University of Missouri, Rolla, MO
Combinatorial rigidity in complex dynamics
Abstract: A beautiful aspect of complex dynamics is the abundance of combinatorial rigidity phenomena, that is, instances where the geometry of a dynamical system is faithfully encoded by purely combinatorial information (e.g. a rational number, a homotopy class, a fundamental group,¼). In this talk I'll discuss three manifestations of this rigidity: in the quadratic family z ® z2 + c (Yoccoz); in the family of postcritically finite rational maps (Thurston); and in the family of dynamical Belyi polynomials (P.) I'll also discuss the implications of a very recent result on the failure of rigidity: the combinatorial rigidity conjecture fails for the family of cubic polynomials (Henriksen).

Refreshments at 3:15 pm in Room 321 Altgeld Hall

159 Altgeld Hall, 3:00 p.m.
COMMUTATIVE RING THEORY RAP
Organizational meeting

245 Altgeld Hall, 4:00 p.m.
SPECIAL SEMINAR
Robert Bauer, Georgia Institute of Technology
Construction of heat flows via random holonomy and applications
Abstract: I will explain how to construct geometric heat flows on manifolds through the use of stochastic parallel translation and give applications of this construction to the regularity of heat flows and spectral theory of geometric Laplacians. Some applications are: stochastic characterizations of the Yang-Mills and Yang-Mills heat equation, a new proof of non-explosion for the Yang-Mills heat equation with small initial condition, calculations of the mean of random holonomy and determination of the spectrum of the horizontal Laplacian on the Hopf fibration over complex and quaternionic projective space.

Refreshments at 3:15 pm in Room 321 Altgeld Hall

WEDNESDAY, JANUARY 17

245 Altgeld Hall, 4:00 p.m.
SPECIAL SEMINAR
Eric Sommers, Harvard University
Some open problems in representation theory
Abstract:We describe some open problems in the representation theory of a complex Lie group which are connected to the geometry of nilpotent orbits in the Lie algebra.

Refreshments at 3:15 pm in Room 321 Altgeld Hall

THURSDAY, JANUARY 18

145 Altgeld Hall, 3:00-5:00 p.m.
COLORING THEORY RESEARCH GROUP
Discussion of open problems

243 Altgeld Hall, 3:00 p.m.
COMMUTATIVE RING THEORY
Greg Smith, University of California Berkeley
D-modules on Smooth Toric Varieties
Abstract: Let X be a smooth toric variety. Cox introduced the homogeneous coordinate ring S of X and its irrelevant ideal B. Using the pair (S,B), Cox established that the category of quasi-coherent sheaves on X is equivalent to the category of graded S-modules modulo B-torsion. In particular, this extends Serre's description of sheaves on projective space in terms of graded modules.

In this talk, I will present the D-module version of this result. Specifically, if A denotes the ring of differential operators on Spec(S), then the category of D-modules on X is equivalent to an explicit subcategory of graded A-modules modulo B-torsion. As a consequence, the characteristic variety of a D-module is a geometric quotient of an open subset of the characteristic variety of the associated A-module and holomonic D-modules correspond to holomonic A-modules.

This is joint work with M. Mustata, H. Tsai and U. Walther.

347 Altgeld Hall, 3:00 p.m.
GALOIS MODULES
Organizational meeting

245 Altgeld Hall, 4:00 p.m.
SPECIAL SEMINAR
Yu Yuan, University of Texas at Austin
A Priori Estimates for Fully Nonlinear Elliptic Equations
Abstract: We survey some recent development on a priori estimates for fully nonlinear elliptic equations without convexity. These equations arise in differential geometry, stochastic control theory. Note that the theory of a priori estimates for fully nonlinear equations with convexity condition is well developed.

Refreshments at 3:15 pm in Room 321 Altgeld Hall

FRIDAY, JANUARY 19

314 Altgeld Hall, 2:00 p.m.
SPECIAL SEMINAR
Kevin Ford, University of South Carolina
New results on the distribution of prime numbers
Abstract: In the first part of the talk, we give some numerical improvements for bounds and zero-free regions for the Riemann zeta function, of the Vinogradov-Korobov type. These have direct application to bounds for prime counting functions. The second part deals with subtleties in the distribution of primes in arithmetic progressions, the so-called "prime race problem".

Refreshments at 3:15 pm in Room 321 Altgeld Hall

245 Altgeld Hall, 4:00 p.m.
SPECIAL SEMINAR
Denka Kutzarova-Ford, University of South Carolina
Title: On Tsirelson Type Spaces
Abstract

Refreshments at 3:15 pm in Room 321 Altgeld Hall

243 Altgeld Hall, 4:00 p.m.
MODEL THEORY SEMINAR
Organizational meeting