Seminars and Colloquia by Series

From a formula of Haagerup to random matrices and free probability

Series
Analysis Seminar
Time
Wednesday, November 14, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ionel PopescuGeorgia Tech
This formula of Haagerup gives an expression of the log|x-y| in terms of Chebyshev polynomials of the first kind. This is very useful for problems involving the logarithmic potentials which plays a prominent role in random matrices, free probability, orthogonal polynomials and other areas. We will show how one can go from this to several things, for example the counting problems of planar diagrams and functional inequalities in free probability in particular an intriguing Poincare inequality and some related other inequalities. If time allows I will also talk about a conjecture related to the Hilbert transform, semicircular and arcsine distribution. Parts of this was with Stavros Garoufalidis and some other parts with Michel Ledoux.

Horn inequalities for submodules

Series
Analysis Seminar
Time
Wednesday, November 7, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
005
Speaker
Wing Suet LiMathematics, Georgia Tech

C*-algebras Generated by Composition Operators

Series
Analysis Seminar
Time
Wednesday, October 3, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
In this talk, we investigate the structures of C*-algebras generated by collections of linear-fractionally-induced composition operators and either the forward shift or the ideal of compact operators. In the setting of the classical Hardy space, we present a full characterization of the structures, modulo the ideal of compact operators, of C*-algebras generated by a single linear-fractionally-induced composition operator and the forward shift. We apply the structure results to compute spectral information for algebraic combinations of composition operators. We also discuss related results for C*-algebras of operators on the weighted Bergman spaces.

The Inverse of Two-level Toeplitz Operator Matrices

Series
Analysis Seminar
Time
Wednesday, September 19, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Selcuk KoyuncuDrexel University

Nonlinear transformations of moment sequences

Series
Analysis Seminar
Time
Wednesday, September 12, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Antonio DuranUniversity of Seville
In this talk we discuss some nonlinear transformations between moment sequences. One of these transformations is the following: if (a_n)_n is a non-vanishing Hausdorff moment sequence then the sequence defined by 1/(a_0 ... a_n) is a Stieltjes moment sequence. Our approach is constructive and use Euler's idea of developing q-infinite products in power series. Some others transformations will be considered as well as some relevant moment sequences and analytic functions related to them. We will also propose some conjectures about moment transformations defined by means of continuous fractions.

Similarity results for operators of class C_0

Series
Analysis Seminar
Time
Wednesday, September 5, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Raphael ClouatreIndiana University
The classification theorem for a C_0 operator describes its quasisimilarity class by means of its Jordan model. The purpose of this talk will be to investigate when the relation between the operator and its model can be improved to similarity. More precisely, when the minimal function of the operator T can be written as a product of inner functions satisfying the so-called (generalized) Carleson condition, we give some natural operator theoretic assumptions on T that guarantee similarity.

Uchiyama's lemma and the John-Nirenberg inequality

Series
Analysis Seminar
Time
Wednesday, August 29, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Greg KneseUniversity of Alabama
Using integral formulas based on Green's theorem and in particular a lemma of Uchiyama, we give simple proofs of comparisons of different BMO norms without using the John-Nirenberg inequality while we also give a simple proof of the strong John-Nirenberg inequality. Along the way we prove the inclusions of BMOA in the dual of H^1 and BMO in the dual of real H^1. Some difficulties of the method and possible future directions to take it will be suggested at the end.

About polynomially bounded operators and invariant subspaces

Series
Analysis Seminar
Time
Friday, May 4, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Professor Bernard ChevreauUniversity of Bordeaux 1
In the first part of the talk we will give a brief survey of significant results going from S. Brown pioneering work showing the existence of invariant subspaces for subnormal operators (1978) to Ambrozie-Muller breakthrough asserting the same conclusion for the adjoint of a polynomially bounded operator (on any Banach space) whose spectrum contains the unit circle (2003). The second part will try to give some insight of the different techniques involved in this series of results, culminating with a brilliant use of Carleson interpolation theory for the last one. In the last part of the talk we will discuss additional open questions which might be investigated by these techniques.