Lars Thorge Jensen
I am a Postdoc with Simon Riche
at the University of Clermont Auvergne.
Previously, I was a postdoc at the MSRI for the semester program
Group Representation Theory
and Applications after graduating under the supervision of
Geordie Williamson at the
Max Planck Institute for Mathematics
in Bonn in January 2018.
| Address: |
Laboratoire de Mathématiques Blaise Pascal (UMR 6620)
Université Clermont Auvergne
Campus Universitaire des Cézeaux
3, place Vasarely
TSA 60026 - CS 60026
63178 Aubière Cedex - France
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| Tel: |
+33 4 73 40 76 94 |
| Office: |
1209 |
E-mail:
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lars_thorge.jenxsen(at)uxca.fr
(Remove two letters!)
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Research Interests
My research interests focus on (Geometric) Representation Theory, Categorification and Homological Algebra.
Currently, I am trying to transfer as much as possible from Kazhdan-Lusztig cell theory in characteristic 0 to positive characteristic.
My project is described in more detail in my research proposal, which I wrote
while applying for postdoctoral positions.
Topics which I am interested in and which I am trying to gain a deeper understanding of are:
- the Hecke category and its algebraic and geometric incarnations (Soergel bimodules,
perverse and parity sheaves on flag varieties, equivariant coherent sheaves
on the Steinberg variety),
- representation theory of reductive algebraic groups (in positive characteristic),
- (Affine) flag manifolds, (affine) Grassmannians and the geometry of Schubert varieties,
- the geometric Satake equivalence and the Tannakian formalism,
- Kazhdan-Lusztig cell theory in characteristic 0,
- the 2-braid group and Rouquier complexes,
- Hodge theory.
I am also interested in computational aspects of mathematics, trying to
implement efficient algorithms to calculate the p-canonical basis and p-cells.
Publications and Preprints
- On the induction of p-Cells
Joint with Leonardo Patimo.
We study cells with respect to the p-canonical basis of the Hecke algebra of a crystallographic
Coxeter system (see arXiv:1510.01556,
arXiv:1901.02323) and their compatibility with standard
parabolic subgroups. We show that after induction to the surrounding bigger Coxeter group
the cell module of a right p-cell in a standard parabolic subgroup decomposes as a direct
sum of cell modules. Along the way, we state some new positivity properties of the
p-canonical basis.
- The ABC of p-Cells
Parallel to the very rich theory of Kazhdan-Lusztig cells in characteristic 0, we try to build a similar theory in positive characteristic. We study cells with respect to the p-canonical basis of the Hecke algebra of a crystallographic Coxeter system. Our main technical tool are the star-operations introduced by Kazhdan-Lusztig which have interesting numerical consequences for the p-canonical basis. As an application, we explicitely describe p-cells for symmetric groups using the Robinson-Schensted correspondence. Moreover, we show that Kazhdan-Lusztig cells in finite types B and C decompose into p-cells for p > 2.
- The p-canonical Basis of Hecke algebras
Joint with Geordie Williamson.
In: Categorification and higher representation theory. Vol. 683. Contemp. Math. Amer. Math. Soc.,
Providence, RI, 2017, pp. 333–361.
We describe a positive characteristic analogue of the
Kazhdan-Lusztig basis of the Hecke algebra of a crystallographic
Coxeter system and investigate some of its properties. Using
Soergel calculus we describe an algorithm to calculate this basis.
We outline some known or expected applications in modular representation theory.
We conclude by giving several examples.
- The 2-braid group and Garside normal form
In: Math. Z. 286 (2017), No. 1-2, pp. 491-520.
We investigate the relation between the Garside normal form for positive braids and the 2-braid group defined by Rouquier.
Inspired by work of Brav and Thomas we show that the Garside normal form is encoded in the action of the 2-braid group on a
certain categorified left cell module. This allows us to deduce the faithfulness of the 2-braid group in finite type. We also
give a new proof of Paris' theorem that the canonical map from the generalized braid monoid to its braid group is injective in
arbitrary type.
Talks
- Novembre 2019: The ABC of p-Cells,
Séminaire d'algèbre and géométrie, Laboratoire de Mathématiques Nicolas Oresme, Université de Caen.
- October 2019: The ABC of p-Cells,
Séminaire d'algèbre, Institut Camille Jordan, Lyon, France.
- July 2019: The ABC of p-Cells,
Workshop on Interactions between Representation Theory and Model Theory,
University of Kent, Canterbury, Great Britain.
- December 2018: Survey on Character Formulas for Reductive Algebraic Groups,
Groups, Arithmetic and Algebraic Geometry Seminar, EPFL, Lausanne, Switzerland.
- May 2018: The ABC of p-Cells,
Algebra Seminar, University of Oregon, Eugene, USA.
- May 2018: The ABC of p-Cells,
Algebra Seminar, UCLA, Los Angeles, USA.
- April 2018: The ABC of p-Cells,
Representation Theory and Number Theory Seminar, University of Utah, Salt Lake City, USA.
- February 2018: The ABC of p-Cells,
Group Representation Theory and Applications, MSRI, Berkeley, USA.
- May 2017: The 2-braid group and Garside normal form, Séminaire d'algèbre and géométrie,
Laboratoire de Mathématiques Nicolas Oresme, Université de Caen.
- October 2016: The p-canonical basis of Hecke algebras and p-cells, Seminar on Representation
Theory, RIMS, Kyoto, Japan.
- June 2016: Blocks of Schur algebras and algebraic Groups, Max Planck Institute for Mathematics, Bonn.
- May 2016: The p-canonical basis of Hecke algebras, Oberseminar: Algebra, Zahlentheorie und
algebraische Geometrie, Uni Freiburg.
- November 2015: The Hopfological algebra of Khovanov and Qi, Max Planck Institute for Mathematics, Bonn.
- November 2015: The 2-braid group and Garside normal form, Séminaire Quantique, Institut de
Recherche Mathématique Avancée, Université de Strasbourg.
- August 2015: Perverse Sheaves on the Flag Variety and Category O (Part 2), BIREP Summer
School on Koszul Duality, Bad Driburg.
- April 2015: Structure Theory of Reductive Groups, Classification of Simple Modules,
Seminar on the Representation Theory of Reductive Groups in Positive Characteristic,
Max Planck Institute for Mathematics, Bonn.
- October 2014: Series of Survey Talks on Kazhdan-Lusztig Cell Theory, Max Planck Institute for
Mathematics, Bonn.
Here are some slides from one of the talks.
- June 2014: Representations of Quantum Groups for semi-simple Lie Algebras, Summer
School on Quiver Hecke Algebras, Cargèse, Corsica, France.
Other Documents
Link Collection
Homepages of some other post-docs:
Other useful links:
Last update: 27/11/2019