PhD courses offered for the 2021-2022 academic year:

- Quantum field theory: the algebraic approach and the connection to factorisation algebras (Benini, Pinamonti)
- Complex algebraic surfaces (Penegini, Perego)
- Commutative algebra (Conca, Varbaro, reading course)
- Homological algebra (Varbaro)
- Introduction to the arithmetic of Galois representations (Vigni, reading course)
- Topics in the Calculus of Variations: Optimal Transport and Gradient Flows (Di Marino, Mainini)
- Mathematical modelling of biomedical data (Piana)
- Introduction to convex optimization (Villa, Salzo)
- Topics in Mathematics Education (Morselli)

Other courses will be proposed according to the scientific interests of incoming PhD students.

PhD courses offered for the 2020-2021 academic year:

- Mathematical aspects of quantum field theory (Pinamonti)
- Complex algebraic surfaces (Penegini, Perego)
- Commutative algebra (Conca, Varbaro, reading course)
- Homological algebra (Varbaro)
- Topics in the calculus of variations (Di Marino)
- Mathematical modelling of biomedical data (Piana)

PhD courses offered for the 2019-2020 academic year:

- Mathematical aspects of quantum field theory (Pinamonti)
- Complex algebraic surfaces (Penegini, Perego)
- Homology and cohomology (Penegini, Perego)
- Commutative algebra (Conca, Varbaro, reading course)
- Homological algebra (Varbaro)
- Mathematical modelling of biomedical data (Piana)
- Simplicial sets and the Univalence Axiom (Emmenegger)
- Realizability and hyperdoctrines (Pasquali)
- An introduction to 3D geometry processing and shape analysis (Patanè, Biasotti)
- Non-standard analysis (Camerlo)

PhD courses offered for the 2018-2019 academic year:

- Introduction to induced representation theory (De Mari – 1st Semester)
- Integral closure of ideals, normal Hilbert polynomials and local cohomology of Rees algebras (J.K. Verma (IIT Bombay) – 1-30/05/18)
- Methods of Convex Optimization (De Vito, Villa (PoliMI), Salzo (IIT) – 1st Semester)
- The Mathematics of Machine Learning (De Vito, Rosasco – 2nd Semester)
- Scattering problems (Estatico, Piana – 2nd Semester)
- Reading course “Analytic Number Theory” (Perelli)
- Reading course “Computer Age Statistical Inference: Algorithms, Evidence and Data Science” (Riccomagno)
- Reading course “Homological and combinatorial aspects of Commutative Algebra” (Conca, Varbaro)
- Reading course “Mathematical aspects of Quantum Field Theory on curved spacetimes” (Pinamonti)
- Reading course “Introduction to representation theory” (Sasso, Umanità)
- Reading course “Introduction to Galois representations” (Vigni)
- Reading course “Neural networks: from basics to deep learning” (Massone)
- Reading course “Regularization in Banach spaces” (Benvenuto, Estatico)

PhD courses offered for the 2017-2018 academic year:

- Aspects of mathematical physics I (Pinamonti)
- Aspects of mathematical physics II (Martinetti)
- Introduction to induced representation theory (De Mari)
- Markovian quantum semigroups (Sasso, Umanità)
- Number Theory (Perelli)
- Online learning and Bayesian analysis (P. Alquier, organized by Pontil)
- Reading course on machine learning (Massone)
- Topics in algebraic geometry (Martinetti, Penegini, Vigni)
- Topics in commutative algebra (Conca, Varbaro)

PhD courses offered for the 2016-2017 academic year:

- Advanced topics in commutative algebra (Conca, Rossi, Varbaro)
- Aspects of the Hough transform and its applications (Beltrametti, Massone)
- Internet seminar “Infinite dimensional analysis” (Carbonaro, Mauceri)
- Introduction to theory of group representation (Vigni)
- Introduction to the theory of unitary representation (De Mari, De Viti)
- Methods of the analysis of surfaces and their applications (Biasotti, Patané)
- Mathematical aspects of quantum field theory on curved spacetime (Pinamonti)
- Reading course about analytic number theory (Bettin, Perelli, Righetti)
- Reading course about mathematical logic (Rosolini)