All students from both institutions spend the first year in Padova and the second year in PSL.
Three standard programs are available:
A – Program in Analysis
B – Program in Probability and Finance
C – Program in Probability and Statistical Mechanics
Individual study Programs are also possible, see details below.
The following study programs are for actual MAPPA students, enrolled for the academic years 2023/2025. Minor changes are possible for the 2024/2025 edition.
A – Program in Analysis 2023/2025
First year in Padova
| Year | Semester | Course | Italian SSD | ECTS |
|---|---|---|---|---|
| 1 | I | Differential Geometry | MAT/03 | 8 |
| 1 | I | Introduction to Partial Differential Equations | MAT/05 | 6 |
| 1 | I | Functions Theory | MAT/05 | 8 |
| 1 | I | Stochastic Analysis | MAT/06 | 7 |
| 1 | I / II | Non-linear Analysis OR Calculus of Variation | MAT/05 | 8 |
| 1 | II | Partial Differential Equations 1 | MAT/05 | 8 |
| 1 | II/I | Partial Differential Equations 2 OR Harmonic Analysis | MAT/05 | 6 |
| 1 | I/II | Dynamical Systems OR Symplectic Mechanics OR Numerical Methods for Differential Equations | MAT/07 - MAT/08 | 6-7 |
| 1 | Student Seminar | 4 |
* at 1st semester
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 PDEs | 6 |
| 2 | I | Introduction to evolution PDEs | 6 |
| 2 | I/II | 4 courses among the following: Numerical methods for deterministic and stochastic problems, Introduction to control theory, Mean field games theory, Variational problems and optimal transport in economy, Continuous optimization, Entropy methods, functional inequalities and applications | 24 |
| 2 | II | Research internship + final dissertation | 24 |
* These courses can 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 2023/2025
First year in Padova
| Year | Semester | Course | Italian SSD | ECTS |
|---|---|---|---|---|
| 1 | I | Differential Geometry | MAT/03 | 8 |
| 1 | I | Introduction to Partial Differential Equations | MAT/05 | 6 |
| 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 | Numerical methods for deterministic and stochastic control | 6 |
| 2 | I/II | 5 courses among the following: Jump processes; Stochastic control; Monte Carlo and finite difference methods with applications in finance; Valuation of financial assets by absence of arbitrage; Machine learning in finance; Mean-field game theory; Pathwise techniques in stochastic analysis: rough paths & Co. | 30 |
| 2 | II | Research internship + final dissertation | 24 |
* These courses can 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 2023/2025
First year in Padova
| Year | Semester | Course | Italian SSD | ECTS |
|---|---|---|---|---|
| 1 | I | Differential Geometry | MAT/03 | 8 |
| 1 | I | Introduction to Partial Differential Equations OR Function Theory | MAT/05 | 6-8 |
| 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 | Introduction to mathematical statistical mechanics | 6 |
| 2 | I/II | 4 courses among the following: Harmonic functions and random walks, Integrable probability and the KPZ universality class, Jump processes, Mixing times of Markov chains, Numerical methods for deterministic and stochastic problems, Pathwise techniques in stochastic analysis: rough paths & Co, Random geometric models, Random operators | 24 |
| 2 | II | Research internship + final dissertation | 24 |
* These courses can 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 – Individual study Programs
Individual study programs can be presented during the first semester of the program.
Please contact Prof. Cirant and Fontana in Padova or Prof. Toninelli in PSL to prepare your plan.
Remark that all individual programs need to comply with Annex 1 of the MAPPA agreement.