WEDNESDAY, SEPTEMBER 7, 2005

MATH ECOLOGY SEMINAR

TIME: 3:30 – 4:30 p.m.
ROOM: 575 Dabney
PRESENTERS: Professor Lou Gross and Ms. Clara Logan
TITLE: Individual Based Models


ALGEBRA SEMINAR

TIME: 3:35 p.m.
ROOM: 214 Ayres
SPEAKER: Sudhir Ghorpade, Visiting Faculty
TITLE: Linear Codes and Projective Varieties
ABSTRACT: I will begin with a brief introduction to the theory of linear error correcting codes. We will then discuss an alternative approach to the study of linear codes via projective systems, introduced by Tsfasman and Vladut. Next, we will consider a basic combinatorial problem about the enumeration of an optimal class of linear codes, called MDS codes. While the problem is open in general, some of the known results will be outlined. This problem is naturally related to Grassmannians and their linear sections, and I will outline the connection and indicate some geometric applications. In a related pursuit, we will consider linear codes associated to Grassmannians and their Schubert subvarieties. Some known results and conjectures concerning these will be discussed.

Throughout this series of lectures an attempt will be made to keep the prerequisites to a minimum. In particular, for the first lecture it should suffice to know what a finite field is and what vector spaces are.

ANALYSIS SEMINAR

TIME: 3:35 – 4:25 p.m.
ROOM: 309B Ayres
SPEAKER: Professor Carl Sundberg
TITLE: Zeros of functions in weighted Bergman spaces

THURSDAY, SEPTEMBER 8, 2005

PROBABILITY SEMINAR
The format of the Probability Seminar this semester will be as follows:
Each member of the Probability group will present three/four (perhaps more) lectures describing results and problems of his research area(s). The level of the lectures will be such that these would be accessible to graduate students with probability background.

TIME: 1:10 – 2:00 p.m.
ROOM: 209A Ayres
SPEAKER: Professor Balram S. Rajput
TITLE: Uniform Comparison of Tail Probabilities of (Non-Symmetric) Random
Vectors and Their Symmetrized Counterparts with Applications
ABSTRACT: Let B be a separable Banach space, and X a class of B-valued random vectors (r.v.’s). We shall provide two sufficient conditions (one in terms of certain quantiles and the other in terms of certain moments) for the “uniform comparison” of the tail probabilities of every element of X and its symmetrized counterpart. As a corollary to this result, we shall show that several well known & important classical results that are valid for symmetric (but not for general non-symmetric) B-valued r.v.’s do indeed hold for the r.v.’s belonging to the class X satisfying any of the above noted conditions and another additional convolution condition. These results include the Lévy Inequality, the Kwapie Contraction Principle, and a part of the Ito-Nisio Theorem. We shall further show that the noted required conditions are satisfied by the class of all centered log-concave B-valued
r.v.’s as well as by the class of all strictly a-stable (or more general (r, a)-semi-stable B-valued r.v.’s provided a ¹1 thus proving that all the noted results hold for these classes of r.v.’s. We will also show that for these classes of r.v.’s the constants appearing in the tail probability comparison theorem do not depend on the Branch spaceB in fact, these are universal constants in the log-concave case, and depend only on a in the stable case and on r and a in the semi-stable case. We shall further discuss the tail probability comparison of multi-linear forms in stable/semi-stable r.v.’s and those in theirsymmetrized counterparts; these provide further applications to the study of multiple stochastic integrals relative to stable/semi-stable random measures.


FRIDAY, SEPTEMBER 9, 2005

TOPOLOGY SEMINAR

TIME: 12:20 – 1:10 p.m.
ROOM: 209B Ayres
SPEAKER: Mr. Atish Mitra
TITLE: Asymptotic Dimensions of Metric Spaces – II