Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Larry Rolen
Affiliation:

Vanderbilt University/MPIM
Date:

Wed, 16/02/2022 - 14:30 - 15:30 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.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/246