All students from both institutions spend the first year in Padova and the second year in PSL.
Four standard curricula are available:
A – Program in Analysis
B – Program in Probability and Finance
C – Program in Probability and Statistical Mechanics
D – Program in Probability, Statistics and Data Science
In addition, it is possible to choose study programs at the interface of Analysis, Probability, and Statistics through individual study programs, see details below.
The following study programs are for actual MAPPA students, enrolled for the academic years 2025/2027. Minor changes are possible for the 2026/2028 edition.
A – Program in Analysis 2025/2027
First year in Padova
| Year | Semester | Course | Italian SSD | ECTS |
|---|---|---|---|---|
| 1 | I | Differential Geometry | MAT/03 | 8 |
| 1 | I | Functions Theory | MAT/05 | 8 |
| 1 | I | Stochastic Analysis | MAT/06 | 7 |
| 1 | I | Functional Analysis OR Non-linear Analysis | MAT/05 | 8 |
| 1 | II | Partial Differential Equations 1 | MAT/05 | 8 |
| 1 | II/I | Two courses among: Partial Differential Equations 2; Harmonic Analysis; Calculus of Variations | MAT/05 | 6 + 6 |
| 1 | I/II | One course among: Dynamical Systems; Symplectic Mechanics; Numerical Methods for Differential Equations | MAT/07 - MAT/08 | 6-7 |
| 1 | Student Seminar | 4 |
Second year in PSL
| Year | Semester | Course | ECTS |
|---|---|---|---|
| 2 | I | Recommended: A review of differential calculus for ODEs and PDEs | 0 |
| 2 | I | Recommended: A review of functional analysis tools for PDEs | 0 |
| 2 | I | Introduction to non-linear elliptic PDEs | 6 |
| 2 | I | Introduction to evolution PDEs | 6 |
| 2 | II | Variational problems and optimal transport | 6 |
| 2 | I/II | 4 courses among the following (*): Introduction to dynamical systems; Continuous optimization; Finite difference and Monte-Carlo methods for PDEs; Introduction to control theory; Spectral geometry: isoperimetric inequalities and shape optimization; Spectral theory and variational methods; Introduction to hyperbolic systems of conservation laws; Entropy methods, functional inequalities and applications | 24 |
| 2 | II | Research internship + final dissertation | 18 |
* Elective courses can also be chosen in the list of PSL courses or from other M2 programs in Paris, with the agreement of the supervisor. More courses are available here.
B – Program in Probability and Finance 2025/2027
First year in Padova
| Year | Semester | Course | Italian SSD | ECTS |
|---|---|---|---|---|
| 1 | I | Differential Geometry | MAT/03 | 8 |
| 1 | I | Functions Theory | MAT/05 | 8 |
| 1 | I | Stochastic Analysis | MAT/06 | 7 |
| 1 | I | Introduction to Stochastic Processes | MAT/06 | 8 |
| 1 | II | Advanced Stochastic Processes | MAT/06 | 7 |
| 1 | II | Numerical methods for differential equations | MAT/08 | 7 |
| 1 | II | Partial Differential Equations 2 | MAT/05 | 6 |
| 1 | II | Stochastic methods for finance | MAT/06 - SECS-S/06 | 7 |
| 1 | Student Seminar | 4 |
Second year in PSL
| Year | Semester | Course | ECTS |
|---|---|---|---|
| 2 | I | Recommended: A review of differential calculus for ODEs and PDEs | 0 |
| 2 | I | Recommended: A review of probability theory foundations | 0 |
| 2 | I | Stochastic calculus | 6 |
| 2 | I | Monte Carlo and finite difference methods with applications to finance | 6 |
| 2 | I | Continuous-time Markov processes | 6 |
| 2 | I/II | 4 courses among the following (*): Valuation of financial assets and arbitrage; Machine learning in finance; Stochastic control; Rough paths and SDEs; Analysis in spaces of measures and mean field control/games; Variational problems and optimal transport | 24 |
| 2 | II | Research internship + final dissertation | 18 |
* Elective courses can also be chosen in the list of PSL courses or from other M2 programs in Paris, with the agreement of the supervisor. More courses are available here.
C – Program in Probability and Statistical Mechanics 2025/2027
First year in Padova
| Year | Semester | Course | Italian SSD | ECTS |
|---|---|---|---|---|
| 1 | I | Differential Geometry | MAT/03 | 8 |
| 1 | I | Functions Theory | MAT/05 | 8 |
| 1 | I | Stochastic Analysis | MAT/06 | 7 |
| 1 | I | Introduction to Stochastic Processes | MAT/06 | 8 |
| 1 | II | Advanced stochastic processes | MAT/06 | 7 |
| 1 | II | Numerical Methods for Differential Equations | MAT/08 | 7 |
| 1 | II | Partial Differential Equations 1 | MAT/05 | 8 |
| 1 | II | Symplectic Mechanics OR Advanced Mathematical Physics | MAT/07 | 6 |
| 1 | Student seminar | 4 |
Second year in PSL
| Year | Semester | Course | ECTS |
|---|---|---|---|
| 2 | I | Recommended: A review of probability theory foundations | 0 |
| 2 | I | Limit theorems and large deviations | 6 |
| 2 | I | Continuous-time Markov processes | 6 |
| 2 | II | Introduction to statistical mechanics | 6 |
| 2 | I/II | 4 courses among the following (*): Integrable probability and the KPZ universality class; Random walks and random media; Random interlacements and Gaussian free field; Concentration of measures and related topics; Determinantal processes, random matrices and hyperuniformity; Stochastic calculus | 24 |
| 2 | II | Research internship + final dissertation | 18 |
* Elective courses can also be chosen in the list of PSL courses or from other M2 programs in Paris, with the agreement of the supervisor. More courses are available here.
D – Program in Probability, Statistics and Data Science 2025/2027
First year in Padova
| Year | Semester | Course | Italian SSD | ECTS |
|---|---|---|---|---|
| 1 | I | Differential Geometry | MAT/03 | 8 |
| 1 | I | Functions Theory | MAT/05 | 8 |
| 1 | I | Stochastic Analysis | MAT/06 | 7 |
| 1 | I | Introduction to Stochastic Processes | MAT/06 | 8 |
| 1 | I | High-dimensional Probability for Data Science | MAT/06 | 6 |
| 1 | I | Statistical Methods for High-dimensional Data | SECS-S/01 | 6 |
| 1 | II | Numerical Methods for Differential Equations | MAT/08 | 6 |
| 1 | II | Harmonic Analysis OR Partial Differential Equations 2 | MAT/05 | 6 |
| 1 | Student seminar | 4 |
Second year in PSL
| Year | Semester | Course | ECTS |
|---|---|---|---|
| 2 | I | Recommended: A review of differential calculus for ODEs and PDEs | 0 |
| 2 | I | Recommended: A review of probability theory foundations | 0 |
| 2 | I | Stochastic calculus | 6 |
| 2 | I | Foundations of machine learning | 6 |
| 2 | I | Bayesian statistics | 6 |
| 2 | I/II | 4 courses among the following (*): High-dimensional statistics; Dimension reduction and manifold learning; Introduction to generative modeling with flows and diffusions; Continuous-time Markov processes; Continuous optimization; Variational problems and optimal transport | 24 |
| 2 | II | Research internship + final dissertation | 18 |
* Elective courses can also be chosen in the list of PSL courses or from other M2 programs in Paris, with the agreement of the supervisor. More courses are available here.
E – Individual study programs
Study programs at the interface of Analysis, Probability and Statistics and individual study programs can be defined during the first semester of the MAPPA program. In the first year, students have the possibility of attending selected courses from the MSc in Data Science and from the MSc in Computational Finance at the University of Padova.
Please contact Prof. M. Cirant and C. Fontana in Padova or Prof. A. Florio in PSL to define your study plan. Please note that all individual study programs are subject to approval and should comply with Annex 1 of the MAPPA agreement.