# Algebra Seminar

Date:

10/13/2021 - 2:00pm to 3:00pm

Location:

POT 745

Speaker(s) / Presenter(s):

Fernando Xuancheng Shao, University of Kentucky

Type of Event (for grouping events):

Title: Singmaster's conjecture in the interior of Pascal's triangle

Abstract: Singmaster's conjecture asserts that every natural number greater than one occurs at most a bounded number of times in Pascal's triangle. In this talk I will survey some results on this conjecture, and present a new result which establishes this conjecture in the interior region of Pascal's triangle. Our proof methods combine an Archimedean argument (due to Kand and reminiscent of the Bombieri-Pila determinant method) and a non-Archimedean argument based on Vinogradov's exponential sum estimates over primes. This is joint work with Kaisa Matomaki, Maksym Radziwill, Terence Tao, and Joni Teravainen.