Research

During my PhD (2021-2024), my research explored the use of geometric methods in modular representation theory of algebraic groups.  The motivating project was to find a new proof for the description of the blocks in the category of representations of a reductive algebraic group (over a field of positive characteristic), by using the geometric Satake equivalence and Smith-Treumann theory as developped by Riche-Williamson. I was then working on getting an incarnation of the category of  G1T-modules in terms of perverse sheaves, by adapting the work of Arkhipov-Bezrukavnikov-Braverman-Gaitsgory-Mirkovic. 

Here is a my thesis.

Publication

E. Zabeth, Block decomposition via the geometric Satake equivalence. Annales de l’Institut Fourier (2026). Available here. 

 Talks

• Definition of the dual group and the Satake isomorphism. Talk for the Clermont-Darmstadt  workshop on the Geometric Satake Equivalence (January 2022).

• Block decomposition via the geometric Satake equivalence.  Talks concerning the result of my preprint, given at : the algebra seminar in Clermont (October 2022), the Austms meeting in Sydney (December 2022), and a conference on representation theory in Lyon  (June 2023).

• Jantzen’s Generic Decomposition Patterns and periodic polynomials. Two talks concerning representation theory and Kazhdan-Lusztig combinatorics, given at the Informal Friday Seminar in Sydney (November 2022).