Image: The Kansas State University Department of Mathematics is hosting a Women Lecture Series in celebration of the 50th anniversary of the Association for Women in Mathematics. The series includes Distinguished Lectures and colloquium talks by women mathematicians planned throughout 2021. The talks will be streamed live during Spring 2021 and may be streamed live and/or in person during Fall 2021, depending on the circumstances of the pandemic. The talks will be held at 2:30pm-3:20pm Central Time on a Tuesday or a Thursday; there will be time for Q&A at the end of each talk. See the Spring 2021 schedule at https://www.math.k-state.edu/events/wls/ COLLOQUIUM TALK BETSY STOVALL (University of Wisconsin - Madison) Tuesday, March 30th, 2021, 2:30pm (Central Time) Streamed live: https://youtu.be/u2kW4PTRxek (No registration or sign in needed, unless you would like to ask questions through the chat; in that case, you must login with a gmail account.) Title: Maximizers and near-maximizers for Fourier restriction inequalities Abstract: Fourier restriction phenomena allow us to make sense out of the restriction of the Fourier transform of an Lp function (nominally only defined almost everywhere) on measure zero sets, provided these sets possess sufficient curvature. In the dual formulation, "tubes" whose directions are restricted to lie along some curved set can only overlap with one another on a relatively small region of space. More quantitatively, such phenomena are reflected by Lebesgue space bounds for the Fourier restriction operator. In this talk, we will describe some open questions and recent results regarding the existence of functions that provide a worst-case scenario by saturating these Lebesgue space bounds. Betsy Stovall earned her Ph.D. in Mathematics from the University of California at Berkeley in 2009, continued to an NSF postdoctoral fellowship at UCLA, and is currently an associate professor and L&S Mary Herman Rubenstein Professor at the University of Wisconsin-Madison, where she has been since 2012. Her research focuses on the interactions between curvature and two of the fundamental operators of harmonic analysis: convolution and the Fourier transform. A recurrent theme of her work has been to prove new inequalities by precisely quantifying their near counter-examples.
