Jonathan Gruber I am a postdoctoral researcher at Friedrich-Alexander University Erlangen-Nuremberg, in the working group of Peter Fiebig. Previously, I was a postdoc at the University of York (working with Chris Bowman and Stephen Donkin) and a research fellow at the National University of Singapore (in the working group of Huanchen Bao). I completed my PhD at the École Polytechnique Fédérale de Lausanne in 2022; my PhD advisor was Donna Testerman. email: jonathan.gruber at fau.de Here is a picture of me.

Research My reseach interest is broadly in representation theory, and more specifically in the following topics: - representations of reductive algebraic groups and related topics; - tilting objects in highest weight categories; - homological methods in representation theory; - tensor categories, tensor ideals; - (diagrammatic) categorification; - Coxeter groups, Hecke algebras, Soergel bimodules. Articles and preprints: preprint Multiplicity free and completely reducible tensor products for SL₃(k) and Sp₄(k). preprint Generic direct summands of tensor products for simple algebraic groups and quantum groups. articlepreprint Linkage and translation for tensor products of representations of simple algebraic groups and quantum groups, Proc. London Math. Soc., 129(4), e12641. articlepreprint Tensor ideals for quantum groups via minimal tilting complexes, Proc. Amer. Math. Soc., 152(03), 967-975. articlepreprint Cohomology in singular blocks of parabolic category O, Glasg. Math. J., 65(3), 555-568. articlepreprint On minimal tilting complexes in highest weight categories, Algebr. Represent. Theory, 26(6), 2753-2783. articlepreprint Coxeter combinatorics for sum formulas in the representation theory of algebraic groups, Rep. Theory 26, 68-93. articlepreprint On complete reducibility of tensor products of simple modules over simple algebraic groups, Trans. Amer. Math. Soc. Ser. B 8, 249-276. My PhD thesis is available here: PhD thesis Generic direct summands of tensor products for simple algebraic groups and quantum groups at roots of unity.

Conferences I am involved or have been involved in the organization of the following conferences. Groups and Representation Theory in Lausanne EPFL, November 19-21, 2024 website Diagrammatic Intuition and Deep Learning in Mathematics University of York, July 15-19, 2024 website Combinatorial representation theory and diagrammatic categorification University of York, July 8-12, 2024 website Young Algebraists' Conference EPFL, September 6-10, 2021 website

Teaching In Semester 2 of the academic year 2022 / 2023, I was teaching a course on tensor categories at NUS. The lecture notes and exercises are available here: lecture notes exercises