Thomas Gerber
EPFL SB MATH GR-TES
MA C3 614 (Bâtiment MA)
Station 8
CH-1015 Lausanne
Web site: Web site: https://gr-tes.epfl.ch/
EPFL AVP-PGE EDMA-ENS
MA B2 424 (Bâtiment MA)
Station 8
CH-1015 Lausanne
+41 21 693 54 73
Office:
MA B2 424
EPFL
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EDMA-ENS
AGEPoly - Musical
P.a. AGEPoly
Esplanade EPFL
Station 9
CH-1015 Lausanne
About me
I am an SNSF Ambizione research fellow in the Testerman group.Before this, I was a research and teaching assistant in the group of Gerhard Hiss at the Lehrstuhl D für Mathematik in Aachen.I completed my PhD in Tours under the supervision of Cédric Lecouvey and Nicolas Jacon.
See my CV for more information.
Publications
Selected publications
| Thomas Gerber, Jérémie Guilhot, Cédric Lecouvey 2021, arXiv:2110.04029. |
Generalised Howe duality and injectivity of induction: the symplectic case |
| Thomas Gerber, Cédric Lecouvey To appear in Annales de l'Institut Henri Poincaré D (Combinatorics, Physics and their Interactions) |
Duality and bicrystals on infinite binary matrices |
| Maciej Dołęga, Thomas Gerber, Jacinta Torres Journal of Algebra 560 (2020), Pages 1253-1296 |
A positive combinatorial formula for symplectic Kostka-Foulkes polynomials I: Rows |
| Thomas Gerber, Nicolas Jacon, Emily Norton Pacific Journal of Mathematics 306 (2020), No. 2, 487–517 |
Generalized Mullineux involution and perverse equivalences |
| Thomas Gerber 2018. arXiv:1809.09519 (not for publication) |
Cylindric multipartitions and level-rank duality |
| Thomas Gerber Journal of Algebraic Combinatorics 49 (2019), 99-124 |
Heisenberg algebra, wedges and crystals |
| Thomas Gerber, Emily Norton Journal of Combinatorial Algebra 2 (2018), 103-145 |
The sl∞-crystal combinatorics of higher level Fock spaces |
| Thomas Gerber Advances in Mathematics 329 (2018), 916-954 |
Triple crystal action in Fock spaces |
| Thomas Gerber, Gerhard Hiss Communications in Algebra 45 (2016), 561-574 |
Branching graphs for finite unitary groups in non-defining characteristic |
| Thomas Gerber, Gerhard Hiss, Nicolas Jacon International Mathematics Research Notices 22 (2015), 12206-12250 |
Harish-Chandra series in finite unitary groups and crystal graphs |
| Thomas Gerber Algebras and Representation Theory 18 (2015), 1009-1046 |
Crystal isomorphisms in Fock spaces and Schensted correspondence in affine type A |
| Thomas Gerber Journal of Algebra 413 (2014), 364-401 |
Generalised canonical basic sets for Ariki-Koike algebras |
Research
Topics
I am interested in combinatorial aspects in modular representation theory of reflection groups (and of their associated Hecke algebras), and of finite classical groups.I also investigate questions from Lie theory, including representation theory of quantum groups, seen as deformations of Kac-Moody Lie algebras. In particular, categorification phenomenons (involving e.g. crystals and canonical bases) provide suprising links with the aforementioned groups and algebras.
Research articles
See this list. My research articles can be found on arXiv.PhD thesis
I have defended my PhD thesis entitled Decomposition matrices for Ariki-Koike algebras and crystal isomorphisms in Fock spaces in July 2014. You can find it online here.Programming
I have written a few python programs for computing affine type A crystals using the combinatorics of Fock spaces. Also, I implemented the corresponding crystal isomorphisms, Heisenberg crystals, Mullineux-type maps and an affine Robinson-Schensted correspondence.For any particular request, do not hesitate to write me.
Related mathematicians
Here is a (non-exhaustive) list of some fellow mathematicians whose work I like to keep track of: Chris Bowman, Maria Chlouveraki, Maciej Dołęga, Olivier Dudas, Matthew Fayers, Iain Gordon, Gerhard Hiss, Nicolas Jacon, Alexander Kleshchev, Cédric Lecouvey, Peter Littelmann, Andrew Mathas, Philippe Nadeau, Emily Norton, Loic Poulain d'Andecy, Christoph Schönnenbeck, Peng Shan, Jay Taylor, Donna Testerman, Jean-Yves Thibon, Jacinta Torres.Miscellaneous links
Seminar Groups, Arithmetic & Algebraic Geometry at EPFLSwiss National Science Foundation
International Research Network "Representation theory"
Teaching & PhD
Teaching
Mathematics