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:
- Bachelor in Economics and Mathematics
- Magistère (in French)
- Master’s in Data Science for Social Sciences (D3S)
- Master’s in Mathematics and Economic Decision (MED)
- Master's in Statistics and Econometrics (Econométrie et Statistiques)
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.
Sebastian Engelke (University of Geneva) will give a course in April 2027.
Past advanced courses
- An Introduction to viscosity solutions with applications in Economics by A. Davini: Friday September 12, 22 and 26 from 11am to 12:30pm in Auditorium 6, Monday September 15 and 22 from 11am to 12:30pm in Auditorium 6, Thursday September 18 from 2pm to 5pm in Auditorium 4, and Thursday September 25 from 2pm to 5pm in Auditorium 6, 2025
- Prophet Inequalities by B. Ziliotto : Thursday September 4 from 9:30am to 11am in Auditorium 5, Friday September 5, 12, 26 and October 3 from 9:30am to 11am in 335, Monday September 8 from 9:30am to 11am in 535, Monday September 15, 22, 29 from 9:30am to 11am in 335, 2025
- Diffusion Models in Generative AI by J. Chhor: in Semester 2 after first half of Stochastic Optimal Control in Economics
- Functional Data Analysis by Davy Paindaveine (Université Libre de Bruxelles)
- Strategic Aspects of Bandit Models by Eran Shmaya (Stony Brook University)
- Selected topics in nonsmooth optimization with G Li: Monday September 16, 23, 30 and October 7, 2024 from 9h30 to 12h30.
- Bi-Level Optimization with D. Salas : Wednesday October 16 and 23 from 9h30 to 12h30; Wednesday November 6 from 8h to 11h; Wednesday November 13 and 27 from 9h30 to 12h30.
- Statistical Theory of Deep Learning from February 10 to 14, 2025
- Prophet Inequalities with B. Ziliotto : Tuesday October 1 and 8 from 15h30 to 18h30; Tuesday October 15, 22 and November 5 from 14h to 17h
- Online and Reinforcement Learning with J. Chhor : Semester 2.
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"
Pierre Alquier (Riken AIP) gave courses at TSE on November 2022 "PAC-Bayes and Information bounds, with Applications to Variational Inference"
List of publications
The dual space of a complex Banach space restricted to the field of real numbers
On intertwining relations between Ehrenfest, Yule and Ornstein-Uhlenbeck processes
Induced idleness leads to deterministicheavy traffic limits for queue-basedrandom-access algorithms
On a Stationary Schrödinger Equation with Periodic Magnetic Potential
On interweaving relations
Numerical influence of ReLU’(0) on backpropagation
Nonsmooth Implicit Differentiation for Machine Learning and Optimization
On A Family of Isospectral Pure-Birth Processes
On the evolution by duality of domains on manifolds
Hidden stochastic games and limit equilibrium payoffs
The impact of incorrect social information on collective wisdom in human groups
Collective Information Processing in Human Phase Separation
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