The research lines in our group pertain to the study of mathematical structures emerging from fundamental theoretical physics and interdisciplinary applications. In particular, the group members have interests in:
General relativity and relativistic theories of gravity, including relativistic positioning;
Calculus of variations on fiber bundles and related conservation laws;
Geometric structures on (pseudo-)Riemannian manifolds deriving from string theory and holography (AdS/CFT);
Mathematical methods for the exact non-perturbative study of quantum field theories (e.g. localization and integrability);
Fluid dynamics and optical non-linear models, their integrability and singularities, dispersive and Hamiltonian PDEs;
Geometric-algebraic and qualitative aspects of differential equations of physical, biological and evolutionary interest.
You can learn about these topics (and others) by attending our seminars and special events that we organize regularly.
The Department has several openings for various positions every year. Some of the opportunities to join our group are summarized here.
Forthcoming Events
September 11-12, 2025 - QuanTO Lectures
Title: TBA
Program: TBA
Lecturer: Roberto Longo (Roma 2)
Place and Time: TBA
Organizers: R. Adami, L. Andrianopoli, A.Cavaglià, D. Martelli, M. Meineri, F. Nieri, S. I. Trapasso, M. TrigianteSponsors: PoliTo, UniTo and INFNPast Events
January 30, 2025 - QuanTO Lectures
Title: Bogoliubov Theory for Dilute Bose Gases
Program: I am going to review recent progress in the mathematical understanding of the low-energy properties of dilute quantum systems. In particular, I am going to present a rigorous version of Bogoliubov theory and I am going to show how it can be used to obtain precise estimates for the ground state energy and the low-energy excitation spectrum and also to approximate the time evolution of Bose gases in the so-called Gross-Pitaevskii regime.
Lecturer: Benjamin Schlein (Zürich U.)
Place and Time:
Politecnico di Torino, Aula 1D, 10.00 - 12.00 (crash course)
Math Dept. "G. Peano" UniTo, Aula Magna (Floor 2), 15.00 - 16.00 (seminar)
Organizers: R. Adami, L. Andrianopoli, A.Cavaglià, D. Martelli, M. Meineri, F. Nieri, S. I. Trapasso, M. TrigianteSponsors: PoliTo, UniTo and INFN
September 19-20, 2024 - Mini-Course
Title: Introduction to Non-Invertible Symmetries
Program: These are two introductory lectures on the broad notion of generalized symmetries and their applications to Quantum Field Theory. The covered topics include:
Non-invertible topological lines in (1+1)d Ising CFT and Kramers-Wannier duality;
Selection rules and physical consequences;
High-form global symmetries;
Non-invertible symmetries in (3+1)d QFT, including their relation to the Adler-Bell-Jackiw anomaly.
Ref.s:
- Sub-topics 1 and 2: [arXiv:1802.04445], [arXiv:2308.00747], [arXiv:2307.02534], [arXiv:2401.12281]
- Sub-topics 3 and 4: [arXiv:1412.5148], [arXiv:2204.09025], [arXiv:2205.05086], [arXiv:2205.01104]
The webpage of the season 2023-24 can be found here.