Title: Dyadic analysis (virtually) meets number theory

Abstract: In this talk we discuss two ways in which dyadic analysis and number theory share a rich interaction. The first involves a complete classification of "distinct dyadic systems". These are sets of grids which allow one to compare any Euclidean ball nicely with any dyadic cube, and allow for showing that a large number of continuous objects and operators can be "replaced" with their easier dyadic counterparts. Secondly, we define and make progress on showing the (failure) of a "Hasse principle" in harmonic analysis; specifically, we discuss the interplay between number theory and dyadic analysis that allows us to construct a measure that is "p-adic" doubling for any prime p (in a finite set of primes), yet not doubling overall.

About the Speaker: Theresa (Tess) Anderson recieved her PhD from Brown University supervised by Jill Pipher in 2015 and she was a recipient of  an NSF Graduate Fellowship in Mathematics. She was a Van Vleck Visiting Assistant Professor and an NSF Postdoctoral Fellow at University of Wisonsin at Madison for three years and joined the faculty at Purdue University in 2018 as an Assistant Professor. She has published many papers in excellent venues and she is currently funded by NSF-DMS. Her research  interests are in both harmonic analysis and number theory and particularly their interplay. Some recent work has been in discrete variants of objects and tools from harmonic analysis, lattice point counting including distribution of prime vectors on surfaces, structure theorems in harmonic analysis, and development of Fourier analytic methods in arithmetic statistics.

Tess visited UNM first as a graduate student for several weeks in 2013, then she came to the 2014 AMS Meeting that the Department hosted in the Spring,  and again to the 15th NM Analysis Seminar that we hosted in 2016. A collaboration that started during those visits with David Weirich (UNM PhD 2018) culminated with the publication of a paper in the NYJournal of Math. If she were visiting in person we will take her to Sadie's, since  she loves Southwestern food and specially Sadie's salsa.