Speaker: Prof. Ping Xi (Xi'an Jiaotong University)

Title: Beyond P\'olya--Vinogradov

Time: 14:00-15:00  April 23, 2026 (Thursday)

Place: MCM410

Abstract: Direct applications of Fourier analysis produce the P\'olya--Vinogradov type bounds. However, it is usually very crucial to beat this natural P\'olya--Vinogradov barrier in many applications. In this talk, we will discuss several different occasions that one may go beyond the P\'olya--Vinogradov barrier. In particular, we talk about our recent work on short sums of geometric M\"obius functions (over function fields) and quadrilinear forms of Kloosterman sums (over finite fields), which cannot be reached directly by Riemann Hypothesis over finite fields.