Event Detail

Event Type: 
Department Colloquium
Date/Time: 
Monday, October 18, 2021 - 16:00 to 17:00
Location: 
TBA

Speaker Info

Institution: 
Vanderbilt University
Abstract: 

This talk is for a general audience. I will describe recent work on the integer partition function, which counts the number of ways to break up natural numbers as sums of smaller natural numbers. 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.