Number Theory Seminar

Date: March 2, 2023

Time: 2:30PM - 3:30PM

Location: BLOC 302

Speaker: Larry Rolen, Vanderbilt University

Title: Recent problems in partitions and other combinatorial functions

Abstract: In this talk, I will discuss recent work, joint with a number of collaborators, on analytic and combinatorial properties of the partition and related functions. This includes work on recent conjectures of Stanton, which aim to give a deeper understanding into the "rank" and "crank" functions which "explain" the famous partition congruences of Ramanujan. I will describe progress in producing such functions for other combinatorial functions using the theory of modular and Jacobi forms and recent connections with Lie-theoretic objects due to Gritsenko-Skoruppa-Zagier. I will also discuss how analytic questions about partitions can be used to study Stanton's conjectures, as well as recent conjectures on partition inequalities due to Chern-Fu-Tang and Heim-Neuhauser, which are related to the Nekrasov-Okounkov formula.