Seminars and Colloquia by Series

Wednesday, March 12, 2014 - 14:00 , Location: Skiles 005 , Prabath Silva , Indiana University , Organizer: Brett Wick
In this talk we will discuss applications of a new method of proving vector-valued inequalities discovered by M. Bateman and C. Thiele. We give new proofs of the Fefferman-Stein inequality (without using weighted theory) and vector-valued estimates of the Carleson operator using this method. Also as an application to bi-parameter problems, we give a new proof for bi-parameter multipliers without using product theory. As an application to the bilinear setting, we talk about new vector-valued estimates for the bilinear Hilbert transform, and estimates for the paraproduct tensored with the bilinear Hilbert transform. The first part of this work is joint work with Ciprian Demeter.
Monday, March 10, 2014 - 14:00 , Location: Skiles 171 , Conni Liaw , Baylor University , Organizer: Brett Wick
The Bochner Classification Theorem (1929) characterizes the polynomial sequences $\{p_n\}_{n=0}^\infty$, with $\deg p_n=n$ that simultaneously form a complete set of eigenstates for a second order differential operator and are orthogonal with respect to a positive Borel measure having finite moments of all orders: Hermite, Laguerre, Jacobi and Bessel polynomials. In 2009, G\'{o}mez-Ullate, Kamran, and Milson found that for sequences $\{p_n\}_{n=1}^\infty$, with $\deg p_n=n$ (i.e.~without the constant polynomial) the only such sequences are the \emph{exceptional} Laguerre and Jacobi polynomials. They also studied two Types of Laguerre polynomial sequences which omit $m$ polynomials. We show the existence of a new "Type III" family of Laguerre polynomials and focus on its properties.
Wednesday, February 5, 2014 - 14:00 , Location: Skiles 005 , Bill Ross , University of Richmond , Organizer: Brett Wick
This will be a survey talk on the ongoing classification problem for Carleson and reverse Carleson measures for the de Branges-Rovnyak spaces. We will relate these problems to some recent work of Lacey and Wick on the boundedness of the Cauchy transform operator.
Wednesday, January 22, 2014 - 14:00 , Location: Skiles 005 , Dr. Roman Riser , ETH, Zurich , Organizer: Doron Lubinsky
Abstract: In the beginning, the basics about random matrix models andsome facts about normal random matrices in relation with conformal map-pings will be explained. In the main part we will show that for Gaussianrandom normal matrices the eigenvalues will fill an elliptically shaped do-main with constant density when the dimension n of the matrices tends to infinity. We will sketch a proof of universality, which is based on orthogonalpolynomials and an identity which plays a similar role as the Christoff el-Darboux formula in Hermitian random matrices.Especially we are interested in the density at the boundary where we scalethe coordinates with n^(-1/2). We will also consider the off -diagonal part of thekernel and calculate the correlation function. The result will be illustratedby some graphics.
Wednesday, January 8, 2014 - 15:04 , Location: Skiles 005 , Alden Water , Univesity of Paris , Organizer: Michael Lacey
Wednesday, November 20, 2013 - 15:00 , Location: Skiles 005 , Sofia Ortega Castillo , Texas A&M University , Organizer: Brett Wick
I will introduce the cluster value problem, and its relation to the Corona problem, in the setting of Banach algebras of analytic functions on unit balls. Then I will present a reduction of the cluster value problem in separable Banach spaces, for the algebras $A_u$ and $H^{\infty}$, to those spaces that are $\ell_1$ sums of a sequence of finite dimensional spaces. This is joint work with William B. Johnson.
Wednesday, November 13, 2013 - 15:00 , Location: Skiles 005 , Shahaf Nitzan , Kent State , Organizer: Brett Wick
This talk discusses exponential frames and Riesz sequences in L^2 over a set of finite measure. (Roughly speaking, Frames and Riesz sequences are over complete bases and under complete bases, respectively). Intuitively, one would assume that the frequencies of an exponential frame can not be too sparse, while those of an exponential Riesz sequence can not be too dense. This intuition was confirmed in a very general theorem of Landau, which holds for all bounded sets of positive measure. Landau's proof involved a deep study of the eigenvalues of compositions of certain projection operators. Over the years Landaus technique, as well as some relaxed version of it, were used in many different setting to obtain results of a similar nature. Recently , joint with A. Olevskii, we found a surprisingly simple approach to Landau's density theorems, which provides stronger versions of these results. In particular, the theorem for Riesz sequences was extended to unbounded sets (for frames, such an extension is trivial). In this talk we will discuss Landau's results and our approach for studying questions of this type.
Wednesday, November 6, 2013 - 15:05 , Location: Skiles 005 , Ben Krause , UCLA , Organizer: Michael Lacey
We will discuss the fine notion of the pointwise convergence of ergodic averages in setting where one the ergodic transformation is a Z^d action, and the averages are over more exotic sets than just cubes. In this setting, pointwise convergence does not follow from the usual ergodicity arguments. Bourgain, in his study of the polynomial ergodic averages invented the variational technique, which we extend to our more exotic averages.
Wednesday, May 1, 2013 - 10:07 , Location: Skiles 005 , Yen Do , Yale University , Organizer: Michael Lacey
In this talk I will describe an Lp theory for outer measures, which could be used to connect two themes of Lennart Carleson's work: Carleson measures and time frequency analysis. This is joint work with Christoph Thiele.
Wednesday, April 3, 2013 - 14:00 , Location: Skiles 005 , Sonmez Sahutoglu , University of Toledo , Organizer: Brett Wick
Complex analysis in several variables is very different from the one variable theory. Hence it is natural to expect that operator theory on Bergman spaces of pseudoconvex domains in $\mathbb{C}^n$ will be different from the one on the Bergman space on the unit disk. In this talk I will present several results that highlight this difference about compactness of Hankel operators.  This is joint work with Mehmet Celik and Zeljko Cuckovic.

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