Nicholas Smoot (RISC, Johannes Kepler University, Linz, Austria) - Thursday Nov 3, 2022 - 4:00 PM to 5:00 PM

The talk this week is by Nicholas Smoot from the Research Institute of Symbolic Computation (RISC) at Johannes Kepler University (JKU), Linz, Austria. The announcement is below.

Talk Announcement:

Title:  Partitions, Kernels, and Localization

Speaker: Nicholas A. Smoot (RISC at JKU, Austria)

 

When: Thursday, November 3, 2022 - 4:00 PM - 5:00 PM (IST) 

Where: Zoom. Please write to the organisers if you require the link (sfandnt@gmail.com)

Live Link: https://youtu.be/bXp1LMWTcqY

Tea or Coffee: Please bring your own.

Abstract:  

Since Ramanujan's groundbreaking work, a large variety of infinite congruence families for partition functions modulo prime powers have been discovered. These families vary enormously with respect to the difficulty of proving them. We will discuss the application of the localization method to proving congruence families by walking through the proof of one recently discovered congruence family for the counting function for 5-elongated plane partitions. In particular, we will discuss a critical aspect of such proofs, in which the associated generating functions of a given congruence family are members of the kernel of a certain linear mapping to a vector space over a finite field. We believe that this approach holds the key to properly classifying congruence families.