Chris Bowman: Tensor Products, Modular Representations, and Character Vanishing
Abstract: The representation theory of symmetric and alternating groups is a classical area of study for over 100 years. However, much is still unknown: we have barely scratched the surface of the decomposition problem for products of complex characters; we do not know the dimensions of simple characters in positive characteristic; and even an understanding of the character vanishing sets is out of reach. We will discuss how Christine Bessenrodt's work pushed the boundaries of our understanding of these three problems and her insights regarding the surprising and beautiful connections interrelating them. We will also discuss some of her unpublished conjectures on how these problems might be tackled in the future.
Jørn Olsson: Christine Bessenrodt (1958–2022) – Life and work
Abstract. The first part of the talk will present an overview of Christine Bessenrodt's life and career. The second part will describe some of the main themes of her research, especially those related to the representation theory of the finite symmetric groups and related groups. I will share some remembrances from our scientific collaboration during 30 years.
Haralampos Geranios: On the endomorphism algebra of Specht modules
Abstract: We work in the context of the modular representation theory of the symmetric groups. A standard result of Gordon James states that away from characteristic 2 the endomorphism algebra of the Specht modules is one dimensional. In characteristic 2 the situation changes dramatically: Here the dimension can be arbitrarily large and there is no closed formula available for its calculation. In this talk we will describe an effective way for working out the endomorphism algebra of the Specht modules in even characteristic and highlight several interesting applications of our method.
Sinead Lyle: Rouquier blocks for Ariki-Koike algebras
Abstract: The Rouquier blocks, also known as the RoCK blocks, are important blocks of the symmetric groups algebras and the Hecke algebras of type A, with the partitions labelling the Specht modules that belong to these blocks having a particular abacus configuration. We generalise the definition of Rouquier blocks to the Ariki-Koike algebras, where the Specht modules are indexed by multipartitions, and explore the properties of these blocks.
Stacey Law: A recursive formula for plethysm coefficients and some applications
Abstract: Plethysms lie at the intersection of the representation theory of symmetric groups, algebraic combinatorics and symmetric functions. We give a recursive formula for a family of plethysm coefficients encompassing those involved in Foulkes' Conjecture, and describe some applications to the stability of plethysm coefficients and Sylow branching coefficients for symmetric groups.
Mark Wildon: Modular plethysms of symmetric functions
Abstract: Plethysms of symmetric functions are categorified by polynomial representations of general linear groups. Using ideas from representation theory, de Boeck, Paget and I have discovered new stability results and generalized and unified earlier results on plethysms. In my talk I will concentrate on plethysms categorified by representations of the two-dimensional special linear group and make the connection with a beautiful paper of Bessenrodt on hook lengths in partitions.