Jonathan Gruber
I am a postdoctoral researcher at the University of Bonn. Previously, I was a postdoc at FAU Erlangen-Nuremberg (working with
Peter Fiebig), at the University of York (working with
Chris Bowman and
Stephen Donkin) and 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: gruber at math.uni-bonn.de
Here is a
picture of me.
Research
My research interest is broadly in representation theory, and more specifically in the following topics:
- Lie theoretic representation theory (algebraic groups, quantum group, Lie algebras, etc.);
- highest weight categories and tilting objects;
- homological methods in representation theory;
- tensor categories, tensor ideals;
- (diagrammatic) categorification;
- Coxeter groups, Hecke algebras, Soergel bimodules.
Articles and preprints:
preprint Growth problems in diagram categories, jt. with Dani Tubbenhauer. Some additional material related to this article can be found
here.
preprint Multiplicity free and completely reducible tensor products for SL3(k) and Sp4(k), jt. with Gaëtan Mancini.
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 the fall semester 2025 / 2026, I am organizing a seminar on
Representations of SL2 at the University of Bonn with Johannes Flake. The seminar website is
here.
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