Saturday, November 12, 2022

Nishu Kumari (IISc, Bangalore) - Thursday Nov 17, 2022 - 4:00 PM to 5:00 PM

 Dear all, 

The next talk is by Nishu Kumari, a graduate student in IISc, Bangalore. The announcement is below.

Talk Announcement

Title: Factorization of Classical Characters twisted by Roots of Unity

Speaker: Nishu Kumari (IISc, Bangalore)

When: Thursday, November 17, 2022 - 4:00 PM - 5:00 PM (IST) 

Where: Zoom. Please write to the organisers for the link.

Tea or Coffee: Please bring your own.


Schur polynomials are the characters of irreducible representations of classical groups of type A parametrized by partitions. For a fixed integer $t \geq 2$ and a primitive $t$'th root of unity \omega, Schur polynomials evaluated at elements $\omega^{k} x_i$ for $0 \leq k \leq t-1$ and $1 \leq i \leq n$, were considered by D. J. Littlewood (AMS press, 1950) and independently by D. Prasad (Israel J. Math., 2016). They characterized partitions for which the specialized Schur polynomials are nonzero and showed that if the Schur polynomial is nonzero, it factorizes into characters of smaller classical groups of type A. 

In this talk, I will present a generalization of the factorization result to the characters of classical groups of type B, C and D. We give a uniform approach for all cases. The proof uses Cauchy-type determinant formulas for these characters and involves a careful study of the beta sets of partitions. This is joint work with A. Ayyer and is available here. (Preprint:

Tuesday, November 1, 2022

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 (

Tea or Coffee: Please bring your own.


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.