Emmanuel Kowalski: Harmonic analysis over finite fields and equidistribution (NTWS 097)

Abstract: In 1976, Deligne defined a geometric version of the Fourier transform over finite fields, leading to significant applications in number theory.
For a number of applications, including equidistribution of exponential sums parameterized by multiplicative characters, it would be very helpful to have a similar geometric harmonic analysis for other groups. I will discuss ongoing joint work with A. Forey and J. Fresán in which we establish some results in this direction by generalizing ideas of Katz. I will present the general equidistribution theorem for exponential sums parameterized by characters that we obtain, and discuss applications, as well as challenges, open questions and mysteries.

Original air date:
Thursday, September 9, 2021 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 6pm Israel Daylight Time, 8:30pm Indian Standard Time, 11pm CST)
Friday, September 10, 2021 (1am AEST, 3am NZST)