Seminars and Colloquia by Series

Wednesday, December 5, 2018 - 01:55 , Location: Skiles 005 , Rachel Greenfeld , Bar Ilan University , Organizer: Shahaf Nitzan
Wednesday, November 28, 2018 - 13:55 , Location: Skiles 005 , Rui Han , Georgia Tech , Organizer: Shahaf Nitzan
Wednesday, November 14, 2018 - 13:55 , Location: Skiles 005 , Tao Mei , Baylor University , , Organizer: Michael Lacey
Cotlar’s identity provides an easy (maybe the easiest) argument for the Lp boundedness of Hilbert transforms.   E. Ricard and I  discovered a more flexible version  of this identity, in the recent study of the boundedness of Hilbert transforms on the free groups. In this talk, I will try to introduce this version of Cotlar’s identity and the Lp Fourier multipliers on free groups. 
Wednesday, November 7, 2018 - 10:14 , Location: Skiles 005 , Kelly Bickel , Bucknell University , Organizer: Shahaf Nitzan
Wednesday, October 31, 2018 - 13:55 , Location: Skiles 005 , Joe Fu , UGA , , Organizer: Galyna Livshyts
Wednesday, October 24, 2018 - 13:55 , Location: Skiles 005 , Dmirty Ryabogin , Kent State University , , Organizer: Galyna Livshyts
In  1956, Busemann and Petty  posed a series of questions about symmetric convex bodies, of which only the first one has been solved.Their fifth problem asks the following.Let K be  an origin symmetric convex body in the n-dimensional Euclidean space and let H_x be a hyperplane passing through the origin orthogonal to a unit direction x. Consider a hyperplane G parallel to H_x and supporting to K and let C(K,x)=vol(K\cap H_x)dist (0, G). (proportional to the volume of the cone spanned by the secion and the support point). If  there exists a constant C such that for all directions x we have C(K,x)=C, does it follow that K is an ellipsoid?We give an affirmative answer to this problem for bodies sufficiently close to the Euclidean ball in the Banach Mazur distance.This is a joint work with Maria Alfonseca, Fedor Nazarov and Vlad Yaskin.
Wednesday, October 17, 2018 - 13:55 , Location: Skiles 005 , Longxiu Huang , Vanderbilt University , Organizer: Shahaf Nitzan
Dynamical sampling is a new area in sampling theory that deals with  signals that evolve over time under the action of a linear operator. There are lots of  studies on various aspects of the dynamical sampling problem. However, they all focus on uniform discrete time-sets $\mathcal T\subset\{0,1,2,\ldots, \}$. In our study, we   concentrate on the case   $\mathcal T=[0,L]$. The goal of the present work is to study the frame property of the systems $\{A^tg:g\in\mathcal G, t\in[0,L] \}$. To this end, we also characterize   the completeness and Besselness properties of these systems.
Wednesday, October 10, 2018 - 13:55 , Location: Skiles 005 , Lenka Slavikova , University of Missouri , , Organizer: Michael Lacey
In this talk I will discuss the Mikhlin-H\"ormander multiplier theorem for $L^p$ boundedness of Fourier multipliers in which the multiplier belongs to a fractional Sobolev space with smoothness $s$. I will show that this theorem does not hold in the limiting case $|1/p - 1/2|=s/n$. I will also present a sharp variant of this theorem involving a space of Lorentz-Sobolev type. Some of the results presented in this talk were obtained in collaboration with Loukas Grafakos.
Wednesday, October 3, 2018 - 13:55 , Location: Skiles 005 , Allysa Genschaw , University of Missouri , , Organizer: Michael Lacey
We prove a criterion for nondoubling parabolic measure to satisfy a weak reverse H¨older inequality on a domain with time-backwards ADR boundary, following a result of Bennewitz-Lewis for nondoubling harmonic measure.
Wednesday, September 26, 2018 - 13:55 , Location: Skiles 005 , Suresh Eswarathasan , Cardiff University , Organizer: Shahaf Nitzan
Abstract: Let $(M,g)$ be a compact Riemannian n-manifold without boundary.  Consider the corresponding $L^2$-normalized Laplace-Beltrami eigenfunctions.  Eigenfunctions of this type arise in physics as modes of periodic vibration of drums and membranes. They also represent stationary states of a free quantum particle on a Riemannian manifold.  In the first part of the lecture, I will give a survey of results which demonstrate how the geometry of $M$ affects the behaviour of these special functions, particularly their “size” which can be quantified by estimating $L^p$ norms.     In joint work with Malabika Pramanik (U. British Columbia), I will present in the second part of my lecture a result on the $L^p$ restriction of these eigenfunctions to random Cantor-type subsets of $M$.  This, in some sense, is complementary to the smooth submanifold $L^p$ restriction results of Burq-Gérard-Tzetkov ’06 (and later work of other authors).  Our method includes concentration inequalities from probability theory in addition to the analysis of singular Fourier integral operators on fractals.