Joseph Lehec

Contact

Email: joseph.lehec@univ-poitiers.fr

Address:
LMA
Site du Futuroscope - Téléport 2
11 Boulevard Marie et Pierre Curie
Bâtiment H3 - TSA 61125
86073 POITIERS CEDEX 9

Research

Research Interests

• High-dimensional phenomena in probability and analysis
• Functional inequalities
• Asymptotic theory of convex sets
• Stochastic algorithms

Selected publications

• B., Klartag and J. Lehec, Affirmative Resolution of Bourgain’s Slicing Problem Using Guan’s Bound, Geom. Funct. Anal. 35 (2025), 1147-1168.
  This paper received press coverage from Scientific American.
• B. Klartag and J. Lehec, Isoperimetric inequalities in high-dimensional convex sets, Bull. Amer. Math. Soc. 62 (2025), no. 4, 575-642.
• B. Klartag, and J. Lehec, Bourgain’s slicing problem and KLS isoperimetry up to polylog, Geom. Funct. Anal. 32 (2022), no. 5, 1134-1159.
• S. Bubeck, R. Eldan, and J. Lehec, Sampling from a log-concave distribution with Projected Langevin Monte Carlo, Discrete Comput. Geom. 59 (2018), no. 4, 757-783.
• J. Lehec, Regularization in L1 for the Ornstein-Uhlenbeck semigroup, Ann. Fac. Sci. Toulouse Math. (6) 25 (2016), no. 2, 191-204.
• J. Lehec, Representation formula for the entropy and functional inequalities, Ann. Inst. Henri Poincaré Probab. Stat. 49 (2013), no. 3, 885-899.
• J. Lehec, A direct proof of the functional Santaló inequality, C. R. Acad. Sci. Paris, Ser. I 347 (2009) 55-58.

Publications and preprints

• arXiv
• zbMATH
• HAL
• google scholar

Thesis

• Habilitation thesis (in French)
• PhD thesis (in French)

PhD Students

• Tom Maitre (2024-)
• Pierre Bizeul (2020-23, joint supervision with Dario Cordero-Erausquin).
  Now post-doc at the Weizmann Institute

Recorded talks and slides (selection)

• Slides from a talk given at the opening (general audience) of the 5th Korea-France conference, July 2025.
• Slides for a seminar given at Université de Poitiers, on the solution of Bourgain's slicing problem, May 2025.
• Recordings of a series of lectures given jointly with Bo'az Klartag at an IHP school, May 2024.
• Recording of an online talk at the AGA seminar, May 2022. Related slides.

Some conferences

• Journées MAS 2024
• High dimensional probability and algorithm at ENS
• Journée algorithmes stochastiques à Dauphine

Short Resume

Current position

• Professor, Université de Poitiers.

Past positions

• 2017-2020: Assistant Professor (part-time) at École Normale Supérieure.
• 2009-2022: Assistant Professor, Université Paris-Dauphine.
• 2006-2009: Teaching Assistant, Université Paris-est Marne la Vallée.

Education

• 2016: Habilitation thesis, Université Paris-Dauphine.
• 2008: PhD, Université Paris-Est Marne-la-Vallée, advisor: Bernard Maurey.
• 2002-2006: Student at École Normale Supérieure.

Awards, grants

• 2025: Marc Yor prize
• 2023: ANR grant Conviviality (PI: Max Fathi)
• 2013, 2016, 2021: CNRS sabbatical leaves (demi-délégations)
• 2019: Del Duca Grant (PI: Natael Gozlan)

Teaching documents

The material related to my current classes is only accessible to the students of the University of Poitiers. The documents below correspond to courses I've taught in the past.

• Analyse Convexe (M1) Notes de cours TD1 TD2 TD3 TD4 TD5
• Analyse Complexe (L3) Notes de cours Feuille d'exos
• Intégration et Probabilités (1ère année ENS)
  TD1 TD2 TD3 TD4 TD5 TD6 TD7 TD8 TD9 TD10 TD11 TD12
  
• Systèmes Dynamiques (2ème année ENS)
  TD1 TD2 TD3 TD4 TD5 TD6 TD7 TD8 TD9 TD10 TD11 TD12 TD13
• Processus Discrets (M1) Notes de cours TD1 TD2 TD3 TD4 TD5 TD6 TD7 TD8
• Probabilités(L2) Notes de cours

Last update: Dec. 2025