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 , Tao_Mei@baylor.edu , Organizer: Michael Lacey
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 , johogufu@gmail.com , Organizer: Galyna Livshyts
TBA
Wednesday, October 24, 2018 - 13:55 , Location: Skiles 005 , Dmirty Ryabogin , Kent State University , ryabogin@math.kent.edu , Organizer: Galyna Livshyts
TBA
Wednesday, October 17, 2018 - 13:55 , Location: Skiles 005 , Longxiu Huang , Vanderbilt University , Organizer: Shahaf Nitzan
Wednesday, October 10, 2018 - 13:55 , Location: Skiles 005 , Lenka Slavikova , University of Missouri , slavikoval@missouri.edu , Organizer: Michael Lacey
Wednesday, October 3, 2018 - 13:55 , Location: Skiles 005 , Allysa Genschaw , University of Missouri , adcvd3@mail.missouri.edu , Organizer: Michael Lacey
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.

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