## Seminars and Colloquia by Series

Wednesday, November 19, 2014 - 14:00 , Location: Skiles 006 , Brian Street , University of Wisconsin, Madison , Organizer: Michael Lacey
This talk concerns a theory of "multiparameter singularintegrals."  The Calderon-Zygmund theory of singular integrals is a welldeveloped and general theory of singular integrals--in it, singularintegrals are associated to an underlying family of "balls" B(x,r) on theambient space.  We talk about generalizations where these balls depend onmore than one "radius" parameter B(x,r_1,r_2,\ldots, r_k).  Thesegeneralizations contain the classical "product theory" of singularintegrals as well as the well-studied "flag kernels," but also include moregeneral examples.  Depending on the assumptions one places on the balls,different aspects of the Calderon-Zygmund theory generalize.
Wednesday, November 12, 2014 - 14:00 , Location: Skiles 005 , Diego Maldonado , Kansas State University , Organizer: Brett Wick
We will start with a description of geometric and measure-theoretic objects associated to certain convex functions in R^n. These objects include a quasi-distance and a Borel measure in R^n which render a space of homogeneous type (i.e. a doubling quasi-metric space) associated to such convex functions. We will illustrate how real-analysis techniques in this quasi-metric space can be applied to the regularity theory of convex solutions u to the Monge-Ampere equation det D^2u =f as well as solutions v of the linearized Monge-Ampere equation L_u(v)=g. Finally, we will discuss recent developments regarding the existence of Sobolev and Poincare inequalities on these Monge-Ampere quasi-metric spaces and mention some of their applications.
Wednesday, October 22, 2014 - 14:00 , Location: Skiles 005 , Kelly Bickel , Bucknell University , Organizer: Brett Wick
In this talk, we will discuss a T1 theorem for band operators (operators with finitely many diagonals) in the setting of matrix A_2 weights. This work is motivated by interest in the currently open A_2 conjecture for matrix weights and generalizes a scalar-valued theorem due to Nazarov-Treil-Volberg, which played a key role in the proof of the scalar A_2 conjecture for dyadic shifts and related operators. This is joint work with Brett Wick.
Wednesday, October 15, 2014 - 14:00 , Location: Skiles 005 , Jingbo Xia , SUNY - Buffalo , Organizer: Brett Wick
Wednesday, October 1, 2014 - 14:00 , Location: Skiles 005 , Rishika Rupum , Texas A&M , Organizer: Brett Wick
When does the spectrum of an operator determine the operator uniquely?-This question and its many versions have been studied extensively in the field of inverse spectral theory for differential operators. Several notable mathematicians have worked in this area. Among others, there are important contributions by Borg, Levinson, Hochstadt, Liebermann; and more recently by Simon, Gesztezy, del Rio and Horvath, which have further fueled these studies by relating the completeness problems of families of functions to the inverse spectral problems of the Schr ̈odinger operator. In this talk, we will discuss the role played by the Toeplitz kernel approach in answering some of these questions, as described by Makarov and Poltoratski. We will also describe some new results using this approach. This is joint work with Mishko Mitkovski.
Monday, June 2, 2014 - 14:05 , Location: Skiles 005 , Alexander Aptekarev , Keldysh Institute, Russia , Organizer: Jeff Geronimo
We discuss asymptotics of multiple orthogonal polynomials with respect to Nikishin systems generated by two measures (\sigma_1, \sigma_2) with unbounded supports (supp(\sigma_1) \subset \mathbb{R}_+, supp(\sigma_2) \subset \mathbb{R}_-); moreover, the second measure \sigma_2 is discrete. We focus on deriving the strong and weak asymptotic for a special system of multiple OP from this class with respect to two Pollaczek type weights on \mathbb{R}_+. The weak asymptotic for these polynomials can be obtained by means of solution of an equilibrium problem. For the strong asymptotic we use the matrix Riemann-Hilbert approach.
Wednesday, April 16, 2014 - 14:00 , Location: Skiles 005 , Henri Martikainen , Georgia Tech , Organizer: Brett Wick
We discuss bi-parameter Calderon-Zygmund singular integrals from the point of view of modern probabilistic and dyadic techniques. In particular, we discuss their structure and boundedness via dyadic model operators. In connection to this we demonstrate, via new examples, the delicacy of the problem of finding a completely satisfactory product T1 theorem. Time permitting related non-homogeneous bi-parameter results may be mentioned.
Thursday, April 10, 2014 - 10:00 , Location: Skiles 006 , Ji Li , Macquarie University, Sydney, Australia , Organizer:
We study Hardy spaces on spaces X which are the n-fold product of homogeneous spaces. An important tool is the remarkable orthonormal wavelet basis constructed Hytonen. The main tool we develop is the Littlewood-Paley theory on X, which in turn is a consequence of a corresponding theory on each factor space. We make no additional assumptions on the quasi-metric or the doubling measure for each factor space, and thus we extend to the full generality of product spaces of homogeneous type the aspects of both one-parameter and multiparameter theory involving Littlewood-Paley theory and function spaces. Moreover, our methods would be expected to be a powerful tool for developing function spaces and the boundedness of singular integrals on spaces of homogeneous type. This is joint work with Yongsheng Han and Lesley Ward.
Wednesday, April 9, 2014 - 14:00 , Location: Skiles 005 , Oleg Chalykh , University of Leeds , Organizer: Plamen Iliev
I will discuss a generalization of the KP hierarchy, which is intimately related to the cyclic quiver and the Calogero-Moser problem for the wreath-product $S_n\wr\mathbb Z/m\mathbb Z$.
Wednesday, March 26, 2014 - 14:00 , Location: Skiles 005 , Alex Izzo , Bowling Green State University , Organizer: Brett Wick
A classical theorem of John Wermer asserts that the algebra of continuous functions on the circle with holomophic extensions to the disc is a maximal subalgebra of the algebra of all continuous functions on the circle. Wermer's theorem has been extended in numerous directions.  These will be discussed with an emphasis on extensions to several complex variables.