# Thomas Gerber

### 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 LecouveyCombinatorial Theory 2 (2), #12 (2022) |
Generalised Howe duality and injectivity of induction: the symplectic case |

Thomas Gerber, Cédric LecouveyTo 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 TorresJournal of Algebra 560 (2020), Pages 1253-1296 |
A positive combinatorial formula for symplectic Kostka-Foulkes polynomials I: Rows |

Thomas Gerber, Nicolas Jacon, Emily NortonPacific Journal of Mathematics 306 (2020), No. 2, 487–517 |
Generalized Mullineux involution and perverse equivalences |

Thomas Gerber2018. arXiv:1809.09519 (research note not intended for publication) |
Cylindric multipartitions and level-rank duality |

Thomas GerberJournal of Algebraic Combinatorics 49 (2019), 99-124 |
Heisenberg algebra, wedges and crystals |

Thomas Gerber, Emily NortonJournal of Combinatorial Algebra 2 (2018), 103-145 |
The sl∞-crystal combinatorics of higher level Fock spaces |

Thomas GerberAdvances in Mathematics 329 (2018), 916-954 |
Triple crystal action in Fock spaces |

Thomas Gerber, Gerhard HissCommunications in Algebra 45 (2016), 561-574 |
Branching graphs for finite unitary groups in non-defining characteristic |

Thomas Gerber, Gerhard Hiss, Nicolas JaconInternational Mathematics Research Notices 22 (2015), 12206-12250 |
Harish-Chandra series in finite unitary groups and crystal graphs |

Thomas GerberAlgebras and Representation Theory 18 (2015), 1009-1046 |
Crystal isomorphisms in Fock spaces and Schensted correspondence in affine type A |

Thomas GerberJournal of Algebra 413 (2014), 364-401 |
Generalised canonical basic sets for Ariki-Koike algebras |

### Research

#### Topics

My preferred research topics lie at the interface of representation theory and algebraic combinatorics. I am also interested in interactions with other areas of mathematics. Some themes I like to think about are:- (modular) representations of finite groups (Coxeter groups, finite groups of Lie type, etc),

- Hecke algebras, Cherednik algebras,

- Lie algebras, Kac-Moody algebras and associated quantum groups,

- crystal and canonical bases

- categorification,

- combinatorics on words, RSK correspondence,

- applications in probability (random walks, percolation, etc)

- enumerative combinatorics.

#### Research articles

See the list above. 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"