## Seminars and Colloquia by Series

Wednesday, November 28, 2012 - 14:00 , Location: Skiles 005 , Alden Waters , Jyvaskyla University , Organizer: Michael Lacey
We show how to construct frames for square integrable functionsout of modulated Gaussians. Using the frame representation of the Cauchydata, we show that we can build a suitable approximation to the solutionfor low regularity, time dependent wave equations. The talk will highlightthe relationship of the construction to harmonic analysis and will explorethe differences of the new construction to the standard Gaussian beamansatz.
Wednesday, November 14, 2012 - 14:00 , Location: Skiles 005 , Ionel Popescu , Georgia Tech , , Organizer:
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.
Wednesday, November 7, 2012 - 14:00 , Location: 005 , Wing Suet Li , Mathematics, Georgia Tech , , Organizer:
Consider three partitions of integers a=(a_1\ge a_2\ge ... \ge a_n\ge 0), b=(b_1\ge b_2\ge ... \ge b_n \ge 0), and  c=(c_1\ge \ge c_2\ge ... \ge c_n\ge 0). It is well-known that a triple of partitions (a,b,c) that satisfies the so-call Littlewood-Richardson rule describes the eigenvalues of the sum of nXn Hermitian matricies, i.e., Hermitian matrices A, B, and C such that A+B=C with a (b and c respectively) as the set of eigenvalues of A (B and C respectively). At the same time such triple also describes the Jordan decompositions of a nilpotent matrix T, T resticts to an invarint subspace M, and T_{M^{\perp}} the compression of T onto the M^{\perp}. More precisely, T is similar to J(c):=J_(c_1)\oplus J_(c_2)\oplus ... J_(c_n)$, and T|M is similar to J(a) and T_{M^{\perp}} is similar to J(b). (Here J(k) denotes the Jordan cell of size k with 0 on the diagonal.) In addition, these partitions must also satisfy the Horn inequalities. In this talk I will explain the connections between these two seemily unrelated objects in matrix theory and why the same combinatorics works for both. This talk is based on the joint work with H. Bercovici and K. Dykema. Wednesday, October 17, 2012 - 14:00 , Location: Skiles 005 , Doron Lubinsky , Georgia Tech , , Organizer: Doron Lubinsky Asymptotics for L2 Christoffel functions are a classical topic in orthogonal polynomials. We present asymptotics for Lp Christoffel functions for measures on the unit circle. The formulation involves an extremal problem in Paley-Wiener space. While there have been estimates of the Lp Christoffel functions for a long time, the asymptotics are noew for p other than 2, even for Lebesgue measure on the unict circle. Wednesday, October 10, 2012 - 14:00 , Location: Skiles 005 , Alexander Turbiner , Nuclear Science Institute, UNAM, Mexico , Organizer: Jeff Geronimo A brief overview of some integrable and exactly-solvable Schroedinger equations with trigonometric potentials of Calogero-Moser-Sutherland type is given.All of them are characterized bya discrete symmetry of the Hamiltonian given by the affine Weyl group,a number of polynomial eigenfunctions and eigenvalues which are usually quadratic in the quantum number, each eigenfunction is an element of finite-dimensionallinear space of polynomials characterized by the highest root vector, anda factorization property for eigenfunctions. They admitan algebraic form in the invariants of a discrete symmetry group(in space of orbits) as 2nd order differential operator with polynomial coefficients anda hidden algebraic structure. The hidden algebraic structure for$A-B-C-D$-series is related to the universal enveloping algebra$U_{gl_n}$. For the exceptional$G-F-E\$-seriesnew infinite-dimensional finitely-generated algebras of differential operatorswith generalized Gauss decomposition property occur.
Wednesday, October 3, 2012 - 14:00 , Location: Skiles 005 , Katie Quertermous , James Madison University , Organizer:
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.
Wednesday, September 19, 2012 - 14:00 , Location: Skiles 005 , Selcuk Koyuncu , Drexel University , Organizer: Jeff Geronimo
Wednesday, September 12, 2012 - 14:00 , Location: Skiles 005 , Antonio Duran , University of Seville , Organizer: Jeff Geronimo
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.
Wednesday, September 5, 2012 - 14:00 , Location: Skiles 005 , Raphael Clouatre , Indiana University , Organizer:
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.
Wednesday, August 29, 2012 - 14:00 , Location: Skiles 005 , Greg Knese , University of Alabama , Organizer: Jeff Geronimo
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.