Seminars and Colloquia by Series

One sided bump conditions and two weight boundedness of Calderon-Zygmund operators

Series
Analysis Seminar
Time
Wednesday, February 6, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Alexander ReznikovMichigan State University
We consider a so-called "One sided bump conjecture", which gives asufficient condition for two weight boundedness of a Calderon-Zygmundoperator. The proof will essentially use the Corona decomposition, which isa main tool for a first proof of $A_2$ (also, $A_p$ and $A_p-A_\infty$)conjecture. We will focus on main difficulty, that does not allow to get afull proof of our one sided bump conjecture.

One and Two Weight Theory in Harmonic Analysis

Series
Analysis Seminar
Time
Wednesday, January 30, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
James ScurryGeorgia Tech
We will study one and two weight inequalities for several different operators from harmonic analysis, with an emphasis on vector-valued operators. A large portion of current research in the area of one weight inequalities is devoted to estimating a given operators' norm in terms of a weight's A_p characteristic; we consider some related problems and the extension of several results to the vector-valued setting. In the two weight setting we consider some of the difficulties of characterizing a two weight inequality through Sawyer-type testing conditions.

Boundedness of matrix valued dyadic paraproducts on matrix weighted L^p

Series
Analysis Seminar
Time
Wednesday, January 16, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Josh IsralowitzSUNY Albany
Weighted norm inequalities for singular integral operators acting on scalar weighted L^p is a classical topic that goes back to the 70's with the seminal work of R. Hunt, B. Muckenhoupt, and R. Wheeden. On the other hand, weighted norm inequalities for singular integral operators with matrix valued kernels acting on matrix weighted L^p are poorly understood and results (obtained by F. Nazarov, S. Treil, and A. Volberg in the late 90's) are only known for the situation when the kernel is essentially scalar valued.In this talk, we discuss matrix weighted norm inequalities for matrix valued dyadic paraproducts and discuss the possibility of using our results and a recent result of T. Hytonen to obtain concrete weighted norm inequalities for singular integral operators with matrix kernels acting on matrix weighted L^p. This is joint work with Hyun-Kyoung Kwon and Sandra Pott.

A parametrix construction for the wave equation with low regularity coefficients using a frame of gaussians

Series
Analysis Seminar
Time
Wednesday, November 28, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Alden WatersJyvaskyla University
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.

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
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.

Lp Christoffel Function and Paley-Wiener Spaces

Series
Analysis Seminar
Time
Wednesday, October 17, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Doron LubinskyGeorgia Tech
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.

Solvable Schroedinger equations with trigonometric potentials: From quantum $A_N$ (Sutherland to $E_8$ trigonometric models

Series
Analysis Seminar
Time
Wednesday, October 10, 2012 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Alexander TurbinerNuclear Science Institute, UNAM, Mexico
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.

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
Katie QuertermousJames Madison University
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.

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