Department of Mathematics and Statistics

The Department of Mathematics and Statistics organizes research and teaching in mathematics and statistics at TSE.

It offers a range of programs, from bachelor’s to PhD levels, in mathematics and statistics. It also participates in programs in economics, law, management, and quantitative social sciences at TSE and the University of Toulouse Capitole. Some programs are offered in collaboration with other higher education institutions in Toulouse and internationally.

The research interests of the faculty members include artificial intelligence, calculus of variations, econometrics, game theory, machine learning, operations research, optimization, partial differential equations (PDEs), probability, statistics, and mathematical models in economics, finance, and social sciences.

Faculty members often engage in strong scientific collaborations with the Economics and Social and Behavioral Sciences departments.

The faculty are affiliated with the MADS group at TSE-R (UMR 5314) or IMT-TSE (UMR 5219) for their research. They have received individual prizes and grants (e.g., ANR, CNRS Bronze Medal, ERC, IUF, Lagrange Prize in Optimization, etc.), hold chairs at the Artificial and Natural Intelligence Toulouse Institute (ANITI) and  TIRIS, and serve in numerous editorial roles.

The department offers a Bachelor program in Economics and Mathematics, a Magistère and three Master's programs:

Scholarships are awarded according to academic and individual criteria, see Admission section.

The second year of master MED is the first year of a PhD program in the north American system for those completing a Ph.D. in Mathematics and Statistics at TSE. Our students are regularly granted Ph.D. grants.

All of our programs are certified by the Artificial and Natural Intelligence Toulouse Institute (ANITI). ANITI delivers merit grants for the master students and grants for the research years of the PhD.

Advanced courses in 2026-2027 (Register here)

Next courses

Charles Bertucci (Paris Dauphine) will give a course about Mean-field Models and their Application to Economics in January 2027.

Gaurav Mahajan (a researcher at Mistral AI and an Associate Faculty member at TSE) will give the course Policy Gradient Methods and Large Language Models in April 2027.

-> Syllabus (PDF)

Sebastian Engelke (University of Geneva) will give a course in April 2027.

Past advanced courses

Ingrid Van Keilegom (TSE Visitor) gave a short course on duration analysis with a review of the basics and some more specialized topics on the following dates:

  • Class 1: Monday May 13 from 10 to 12 in T225
  • Class 2: Tuesday May 14 from 1:30 to 3:30 in T225
  • Class 3: Wednesday May 15 from 10 to 12:30 in T225

Title: Duration analysis: review of the basics and some more specialized topics

In this course we started by reviewing the basics of duration analysis (censoring, Kaplan-Meier estimator, Cox model, log-rank test,…) (class 1). Then, more specialized topics have been treated, namely the topic of cure models (class 2) and of dependent censoring (class 3). Cure models are used when the event of interest (e.g. finding a new job) never happens for a proportion of the population, leading to a survival function with a mass at infinity. It is then often of interest to model and estimate separately that mass at infinity and the survival function of those with finite event times, depending on a set of covariates. Dependent censoring means that the duration time and the censoring time are not stochastically independent, whereas usually in duration analysis it is assumed that they are independent. The survival function can in that case not be identified without additional assumptions. Several models will be discussed that lead to (partially) identified survival functions. It has also be seen how the presence of covariates can help to identify the survival function.


Professor Rik Lopuhaä (TSE Visitor) gave a course on February 2024.

Title: Robust estimation of multivariate location and scatter

Abstract: in this course, we discussed several popular methods for robust estimation of multivariate location and scatter including S-estimators and the minimum covariance determinant estimator. We introduced these methods, explain their relationship with M-estimators, and discussed their robustness and asymptotic properties. We also discussed the mathematical techniques that can be used to rigorously derive the properties and features of these methods, and illustrate their implementation in R and how to use them in practice.

Peter Takac (University of Rostock, Germany) gave a course at TSE on February 2023 "Semi-linear and quasi-linear Black-Scholes-type equations in Mathematical Finance: Analytical and numerical methods with some monotonicity"

-> Syllabus (PDF)

Pierre Alquier (Riken AIP) gave courses at TSE on November 2022 "PAC-Bayes and Information bounds, with Applications to Variational Inference"

-> Syllabus (PDF)

List of publications

Factor and Factor Loading Augmented Estimators for Panel Regression With Possibly Nonstrong Factors

Jad Beyhum, and Eric Gautier

Journal of Business and Economic Statistics, vol. 41, n° 1, , pp. 270-281

Numerical Considerations and a New Implementation for Invariant Coordinate Selection

Aurore Archimbaud, Zlatko Drmac, Klaus Nordhausen, Una Radojicic, and Anne M. Ruiz

SIAM Journal on Mathematics of Data Science, vol. 5, n° 1, , pp. 97-121

Many-to-One indirect samplingwith application to the French postaltraffic estimation

Estelle Medous, Camelia Goga, Anne M. Ruiz, Jean-François Beaumont, Alain Dessertaine, and Pauline Puech

The Annals of Applied Statistics, vol. 17, n° 1, , pp. 838-859

Detecting Outliers in Compositional Data Using Invariant Coordinate Selection

In Robust and Multivariate Statistical Methods,

On metastability

Probability Theory and Related Fields, vol. 184, , pp. 275–322

Optimal epidemic suppression under an ICU constraint

Laurent Miclo, Daniel Spiro, and Jörgen W. Weibull

Journal of Mathematical Economics, vol. 101, n° 102669,

Optimal complexity and certification of Bregman first-order methods

Radu Dragomir, Adrien B. Taylor, Jérôme Bolte, and Alexandre D'Aspremont

Mathematical Programming, vol. 194, , pp. 41-83

Swarm gradient dynamics for global optimization: the mean-field limit case

TSE Working Paper, vol. 22-1302,

Detecting outliers in compositional data using Invariant Coordinate Selection

TSE Working Paper, vol. 22-1320,

Finite time extinction for a class of damped Schrödinger equations with a singular saturated nonlinearity

Pascal Bégout, and Jesus Ildefonso Diaz

Journal of Differential Equations, vol. 308, , pp. 252-285

Discrete self-similar and ergodic Markov chains

Laurent Miclo, Pierre Patie, and Rohan Sarkar

The Annals of Probability, vol. 50, n° 6, , pp. 2085-2132

A sublevel moment-SOS hierarchy for polynomial optimization

Tong Chen, Jean-Bernard Lasserre, Victor Magron, and Edouard Pauwels

Computational Optimization and Applications, vol. 81, , pp. 31-66

Job opportunities

Join a vibrant research environment at the Department of Mathematics and Statistics of Toulouse School of Economics (TSE).

TSE recruits a tenure-track Assistant Professor in Nonlinear Stochastic Processes (view details)

We frequently recruit, we encourage you to regularly visit this page.

Contact

Eric Gautier

Department Director

Stéphane Villeneuve

Scientific Deputy Director

Jean Paul Ibrahim

Teaching Deputy Director