Name Reda CHHAIBI
Office Institut de Mathématiques de Toulouse. Université Paul Sabatier. 118, route de Narbonne. F-31062 Toulouse Cedex 9
Email reda.chhaibi -at- math.univ-toulouse.fr
Phone --
Frozen Bubble by Angela Kelly

Welcome to my webpage! I am a mathematician working at the "Institut de Mathématiques de Toulouse" IMT.
Generally speaking, my favorite objects are stochastic dynamics on Lie groups and their interplay with mathematical physics, integrability, random matrices and representation theory.
More on that in the research section.

Usually, my research deals with:

  • - Random walks and Brownian motion on Lie groups.
  • - Representation theory of Lie groups, quantum groups and their combinatorics via crystals.
  • - Mathematical physics and more specifically: Random matrices, particle systems and directed polymers.
A particularly useful tool in all these fields is harmonic analysis, albeit in different guises.

Nevertheless, I am easily swayed away by other scientific topics. For example:

  • - Number theory (link1, link2)
  • - Hörmander's hypoellipticity and rough paths (link)
  • - Machine Learning in relationship with Riemannian geometry (link) or with Free Probability (link)
  • - Quantum measurements (link1, link2)

Here are additionnal (very tempting) topics I am currently thinking about:

  • - Loop groups and quantum groups at roots of unity
  • - Conformal Growth such as DLA and Schramm-Loewner-Kufarev evolutions

Publications

For an up-to-date list of publications, please consult:

phD

"Littelmann path model for geometric crystals, Whittaker functions on Lie groups and Brownian motion"

phD thesis under the direction of Prof. Bougerol , University of Paris VI. Publicly defended on the 24th of January 2013. [arxiv, slides ]. The BIRS video talk below offers an overview, mainly for a public with an algebraic background.

Video talks

Tuesday Oct 15, 2013. 09:07 - 10:08. Banff International Research Station (BIRS), Alberta, Canada. "Archimedean Whittaker functions and geometric crystals". Page link . Video recorded here .

Monday, July 25, 2016 08:59 - 09:45. Banff International Research Station (BIRS), Alberta, Canada. "A probabilistic approach to the Shintani-Casselman-Shalika formula". Page link . Video recorded here .

Slides

This section is mainly for recording purposes. It references some slides and the paper it mainly focuses on. If you are insterested in slides that are not here, do not hesitate to email me.

``A probabilistic approach to the Shintani-Casselman-Shalika formula" [ arxiv, video talk above, slides for an audience of probabilists]

``Whittaker processes as particle systems". [arxiv, slides on probabilistic side only, Based on chapter 6 from thesis]

``On the maximum of the \( C\beta E_n \)". [arxiv, slides in French]

``On the circle, \( GMC^\gamma = \varprojlim C\beta E_n \) for \( \gamma = \sqrt{\frac{2}{β}} \), \( (\gamma \leq 1) \)". [arxiv, slides]

``Quantum \( SL_2 \), Infinite curvature and Pitman's 2M-X theorem." [arxiv, slides]

Visits, conferences and talks

This section is for both recording and organisation purposes. If you are around a place I am visiting, and feel like discussing mathematics, please drop me an email!

02/2019: Aachen-Bochum-Cologne-Darstellungstheorie Seminar [link]. Invited speaker. Aachen, Germany.

01/04/2019: Workshop « Processus stochastiques, géométrie et structures algébriques » [link]. Invited speaker. Mahdia, Tunisia.

10/04/2019: Seminar talk. Queen's University, Kingston, Ontario, Canada.

18/04/2019: Seminar talk. Cornell, USA.

10-21/06/2019: Conference "Probability and quantum field theory: discrete models, CFT, SLE and constructive aspects" [link]. Invited speaker. Porquerolles, France.

17-21//2019: Conference "Extremes in number theory and probability" [link]. Invited speaker. IHP, Paris, France.

09/09/2019: Workshop on quantum measurements. Talk: "Spiking and collapsing in 1d diffusions with large noise". Laboratoire Jean Dieudonné, Nice, France.

14-18/10/2019: Interactions between PDEs and Probability: Particle Systems, Hyperbolic Conservation Laws. [link]. No talk. CIRM, Marseille, France.

22/10/2019: Seminar talk. Geneva, Switzerland.

27-31/10/2019: Workshop. Bristol, UK.

01-15/11/2019: Guest at the Hausdorff Institute. Seminar talk. Bonn, Germany.

17-28/11/2019: Guest at FSU. Seminar and Coloquium talks. Thallahassee, Florida, USA.

02-06/12/2019: XV Latin American Congress of Probability and Mathematical Statistics (CLAPEM 2019). Speaker at a thematic session [link]. Mérida-Yucatán, México.

13/03/2020: Séminaire MeGA. [link]. Paris, France.

19/05/2020: Oxford Random Matrix Theory Seminars. [link]. Online.

25-29/05/2020: Congrès de la SMF [link]. Nancy, France. TO BE CANCELED BECAUSE OF COVID-19.

03-05/06/2020: Workshop ANR MESA "Quantitative methods in Random Matrices" [link]. Toulouse, France. TO BE CANCELED BECAUSE OF COVID-19.

22/09/2020: Seminar Talk. Laboratoire Jean Dieudonné. Nice. France.

2021-2022 - UPS

"Carthagena 2022: Programación 2022 WorkShop en Estadística Aplicada y Ciencia de Datos" [ Link for my course ] [ Link for the course of Camille Male]

"M2 RI: Convergence de mesures de probabilité et transport optimal" [ Page ]

"M1 SID: Modélisation aléatoire" [ Page , Lien Moodle ]

2020-2021 - UPS

"L1 SF: Mathématiques", Amphi H, Groupe de TD H2 (Responsable: LOIZELET Guillaume)

[ Page , Lien Moodle ]

"M1 SID: Modélisation" [ Page , Lien Moodle ]

2019-2020 - UPS

"M1 SID: Modélisation" - Cours/TD/TP

[ TP1 (Corrigé) ] [ TP2 (Corrigé) ] [ TP3 (Corrigé) ] [ TP4 (Corrigé) ] [ TP5 (Corrigé) ] [ CC (Corrigé) ] [ Session 2 ]

"M2 RI: Cours spécialisé" - Growth models and last passage percolation [ Page ]

2017-2018 - UPS

"L1 Sciences: EPNFM1A1 Mathématiques" - Amphi A + Groupe de TDA1. [ Lien moodle ]

"L3 SID: Algèbre linéaire" - Cours/TD

[ Polycopié ] [ TD1 ] [ TD2 ] [ TD3 ] [ TD4 ]

"M1 ESR: Modélisation - Probabilités et statistiques" - Cours/TD/TP

2016-2017 - UPS

"L1: Mathématiques pour la biologie" (Groupe C4). Responsable: CHAPON François.

"L3 SID: Algèbre linéaire" - Cours/TD

"M1 ESR: Modélisation - Probabilités et statistiques" - Cours/TD/TP

2015-2016 - UPS

"L2: Théorie des groupes et géométrie" (Groupe 2). En collaboration avec J. Bertrand, T. Fiedler (Responsable) et L. Gravilov pour les autres groupes.

[ Résumé de cours - Très incomplet ] [ Partiel ] et son [corrigé]. [ Examen ] et son [corrigé].

"M1 ESR: Modélisation - Probabilités et statistiques" - Cours/TD/TP

Fall 2014 - UZH

Introduction to mathematical finance. (Assistant: Martina Dal Borgo).

[ Lecture notes ] [ Sheet 1 ] [ Sheet 2 ] [ Sheet 3 ] [ Sheet 4 ] [ Sheet 5 ] [ Midterm ] [ Sheet 6 ] [ Sheet 7 ] [ Sheet 8 ] [ Sheet 9 ] [ Sheet 10] [ Sheet 11] [ Sheet 12]

Student seminar: Limit theorems in probability theory

Spring 2014 - UZH

Student seminar: Computational methods in mathematics

Fall 2013 - UZH

Introduction to mathematical finance. (Assistant: Doërte Kreher).

[ Midterm ] [ Final ] [ Final correction]

Spring 2013 - UZH

Student seminar: Combinatorics

Fall 2012 - UZH

Introduction to representation theory (Assistant). The course followed the book of Fulton and Harris.

[ Sheet 1 , Solutions ] [ Sheet 2 , Solutions ] [ Sheet 3 , Solutions ] [ Sheet 4 ] [ Sheet 5 ] [ Sheet 6 [ Sheet 7 ] [ Sheet 8 ] [ Exam with solutions ]