Analysis Seminar: Harmonic Analysis over Finite Rings
Speaker: Nathaniel Kingsbury, CUNY Graduate Center
Abstract: Many phenomena in harmonic analysis, such as Salem sets, Sobolev estimates, and restriction estimates, admit discrete analogues over finite fields and the rings Z/p^nZ, which have important and classical interactions with analytic number theory and additive combinatorics. In 2014, Iosevich, Murphy, and Pakianathan studied Kloosterman sums in general, possibly noncommutative, finite rings, and showed that demanding that the hyperbola xy=1 defined over a ring R be a Salem set puts strong constraints on the underlying ring R. In this talk, I will discuss some of my work extending these types of results to other finite rings, and comment on implications for Fourier-analytic conditions as forms of pseudorandomness.
Host: Nic Berkopec