Thomas Gerber

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About me

I am Maître de Conférences (assistant professor) at the Institut Camille Jordan of the Université Lyon 1, member of the Combinatorics and Number Theory group. Before that, I held the following positions:

I completed my PhD in 2014 at Université de Tours under the supervision of Cédric Lecouvey and Nicolas Jacon.

Find more information about me in my CV.

News

Some events I will attend:

Contact

E-mail address: gerber@math.univ-lyon1.fr
Office: Bâtiment Braconnier, office 230
Phone: +33 (0)4 72 43 16 92

Research interests

My research is at the interface of representation theory and algebraic combinatorics. My favourites themes include:

  • modular representation theory of finite groups, representations of Hecke algebras and Cherednik algebras, categorification,
  • Coxeter groups and root systems combinatorics,
  • symmetric polynomials,
  • Lie algebras, Kac-Moody algebras, quantum groups and their representations, crystals and canonical bases,
  • interactions with probability theory.

Research papers

My research articles can also be found on arXiv and on HAL.

  1. Generalised core partitions and Diophantine equations
    With Olivier Brunat and Nathan Chapelier-Laget
    arXiv:2403.11191, 2024 [arXiv]
  2. Atomic length on Weyl groups
    With Nathan Chapelier-Laget
    To appear in Journal of Combinatorial Algebra [arXiv, journal]
  3. Duality and bicrystals on infinite binary matrices
    With Cédric Lecouvey
    Annales de l'Institut Henri Poincaré D (Combinatorics, Physics and their Interactions) 10 (4) (2023) [arXiv, journal]
  4. Generalised Howe duality and injectivity of induction: the symplectic case
    With Jérémie Guilhot and Cédric Lecouvey
    Combinatorial Theory 2 (2) (2022), #12 [arXiv, journal]
  5. A positive combinatorial formula for symplectic Kostka-Foulkes polynomials I: Rows
    With Maciej Dołęga and Jacinta Torres
    Journal of Algebra 560 (2020), 1253-1296 [arXiv, journal]
  6. Generalized Mullineux involution and perverse equivalences
    With Nicolas Jacon and Emily Norton
    Pacific Journal of Mathematics 306 (2020), N°2, 487-517 [arXiv, journal]
  7. Cylindric multipartitions and level-rank duality
    arXiv:1808.06087, 2018 [arXiv] (Notes not intended for publication)
  8. Heisenberg algebra, wedges and crystals
    Journal of Algebraic Combinatorics 49 (2019), 99-124 [arXiv, journal]
  9. The $sl_\infty $-crystal combinatorics of higher level Fock spaces
    With Emily Norton
    Journal of Combinatorial Algebra 2 (2018), 103-145 [arXiv, journal]
  10. Triple crystal action in Fock spaces
    Advances in Mathematics 329 (2018), 916-954 [arXiv, journal]
  11. Branching graphs for finite unitary groups in non-defining characteristic
    With Gerhard Hiss
    Communications in Algebra 45 (2016), 561-574 [arXiv, journal]
  12. Harish-Chandra series in finite unitary groups and crystal graphs
    With Gerhard Hiss and Nicolas Jacon
    International Mathematics Research Notices 22 (2015), 12206-12250 [arXiv, journal]
  13. Crystal isomorphisms in Fock spaces and Schensted correspondence in affine type A
    Algebras and Representation Theory 18 (2015), 1009-1046 [arXiv, journal]
  14. Generalised canonical basic sets for Ariki-Koike algebras
    Journal of Algebra 413 (2014), 364-401 [arXiv, journal]

PhD thesis

  • Decomposition matrices for Ariki-Koike algebras and crystal isomorphisms in Fock spaces (available here).
    Directed by Cédric Lecouvey and Nicolas Jacon, defended on July 1st, 2014.

Programming

I have written a few programs in Sage and GAP in the framework of my research, notably for:

  • computing affine type A crystals (realisation by multipartitions) and certain crystal isomorphisms,
  • computing the Heisenberg crystal and the generalised Mullineux involution,
  • implementing the atomic length on Weyl groups.
Don't hesitate to write me for any particular request.

Current teaching

Previous teaching

Liste des cours

2024–present (Université Lyon 1)

  • Rings and fields
  • Discrete probability and descriptive statistics
  • Basic Mathematical Techniques - Part 1
  • Basic Mathematical Techniques

2024 (EPFL Lausanne)

  • Probability and statistics

2023–2024 (Ruhr University Bochum)

  • Linear algebra
  • Linear algebra (preparatory course)
  • Number theory

2019–2023 (EPFL Lausanne)

  • Galois theory
  • Representation theory
  • Quantum groups and crystal bases

2014–2019 (RWTH Aachen)

  • Modular representation theory
  • Representation theory
  • Linear algebra I
  • Group theory
  • Begleitpraktikum II
  • Algebra
  • Computational algebra
  • Linear algebra II
  • Algebraic topology
  • Topology

2011–2014 (Université de Tours)

  • Probability (5 repeats)
  • Analysis II
  • Analysis I

2010–2011 (Université de Franche-Comté)

  • Linear algebra II
  • Algebra and logic
  • Linear algebra I

Related mathematicians

Olga Azenhas, Olivier Brunat, Nathan Chapelier-Laget, 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, Salim Rostam, Gerhard Röhrle, Peng Shan, Jay Taylor, Donna Testerman, Jean-Yves Thibon, Jacinta Torres.

Mathematical links

Other links