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You are here: FRIAS Fellows Fellows 2020/21 Dr. Leonardo Patimo

Dr. Leonardo Patimo

University of Freiburg
Internal Junior Fellow
October 2020 - July 2021

Room 02 008
Phone +49 (0) 761-203 97340
Fax +49 (0) 761-203 97451


My research interests lie in geometric representation theory. I am particularly interested in aspects of representation theory that can be studied geometrically.

I did my undergrad at University of Pisa and Scuola Normale Superiore. I completed my PhD in 2018 at the Max Planck Institute in Bonn under the supervision of Prof. Geordie Williamson. My thesis focused on the relations between Hodge theory and representation theory.

After that I was a Postdoc  at MSRI in Berkeley during the semester-long program “Group Representation Theory and Applications.” Since June 2018 I am a PostDoc at the university of Freiburg in the group of Prof. Wolgang Soergel.

Publications (Selection)

  • (joint with N. Libedinksy) On the affine Hecke category, preprint, arXiv:2005.02647

  • A combinatorial formula for the coefficient of q in Kazhdan-Lusztig polynomials, Int. Math. Res. Not. IMRN,  arXiv:1811.08184.

  • The Néron-Severi Lie Algebra of a Soergel Module, Transform. Groups 23 (2018), no. 4 , arXiv:1607.05565.

  • The Hard Lefschetz Theorem in positive characteristic for the Flag Varieties, Int. Math. Res. Not. IMRN 2018, no. 18 , arXiv:1608.04202.

  • (joint with L.T. Jensen) On the Induction of p-Cells, preprint, arXiv:1911.0896


Modular Representation Theory and Kazhdan-Lusztig Polynomials

Modular representation theory is the study of representations of groups in positive characteristic. It is an area of mathematics with deep connections with geometry and number theory.

While over the complex numbers representations of semisimple algebraic groups are mostly well understood, we are still far from a satisfactory knowledge of the modular characters of the irreducible representations.

The goal of my project is to push forward our understanding of irreducible representations by studying Kazhdan-Lusztig polynomials and their characteristic p-analogue, the p-Kazhdan-Lusztig polynomials. These polynomials are fascinating objects as they are at the heart of several different character formulas. On the other hand, they are at the moment very hard to compute explicitly. 
However,  in the last decades, new ideas have been thriving in this field and substantial progress has been made. There are several different recent or under development approaches which may help to uncover some of the rich structure of the KL polynomials and, as a consequence, to obtain answers to important open problems in representation theory.