Speaker: Richard Montgomery is affiliated with the Mathematics Institute at the University of Warwick, focusing his research primarily on extremal and probabilistic combinatorics. His work explores fundamental problems in graph theory, including embedding theorems, graph decompositions, and applications of probabilistic methods to establish sharp bounds in combinatorial structures. His research has been recognized through awards such as the European Prize in Combinatorics (2019), the Philip Leverhulme Prize (2020) and the EMS prize (2024), with ongoing support from an ERC Starting Grant. He has the distinction of publishing in top-tier mathematics journals, including JAMS, JEMS, PLMS, JLMS, JCTB, and RSA.

Date: July 4, 2025

Time: 16:00 pm

Location: Zoom Meeting: 875 416 0505 (Password: 042595)

Sponsor: School of Mathematics, Shandong University

Abstract:

A Latin square of order n is an n by n grid filled with n symbols, so that every symbol appears exactly once in each row and each column. A partial transversal of a Latin square of order n is a collection of cells in the grid which share no row, column or symbol, while a full transversal is a transversal with n cells.

The Ryser-Brualdi-Stein conjecture states that every Latin square of order n should have a partial transversal with n -1 elements, and a full transversal if n is odd. In 2020, Keevash, Pokrovskiy, Sudakov and Yepremyan improved the long-standing best known bounds on this conjecture by showing that a partial transversal with n-O (logn/loglogn) elements always exists. I will discuss how to show, for large n, that a partial transversal with n-1 elements always exists.

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/203957.htm