Research Lines 2026-27
| Title | Professor(s) |
|---|---|
| Representation, meaning, and nature of mathematical objects in learning and teacher education. Requirements: Knowledge of mathematics at the university level, basic knowledge of the foundations of mathematics and/or of elementary mathematics from an advanced standpoint, and mathematics education. | Asenova Miglena |
| Inverse boundary value problems for partial differential equations: uniqueness, stability issues and reconstruction algorithms based on artificial intelligence techniques. Requirements: Good knowledge of functional analysis and the theory of weak solutions for partial differential equations and systems. Good knowledge of basic numerical analysis and computer programming. | Aspri Andrea Cavaterra Cecilia Causin Paola |
| Biomathematics and Biostatistics – research line connected with: – Project FAITH – Fighting Against Injustice Through Humanities (strategic project of UniMI) – Project Modeling the heart across the scales: from cardiac cells to the whole organ” PRIN 2017, 2019-2022, PI A. Quarteroni (PoliMI) – Project MICROCARD – “Numerical modeling of cardiac electrophysiology at the cellular scale”, EuroHPC2020, 2021-2024, PI M. Potse (Univ. Bordeaux) – Collaborations with researchers of biomedical areas on: * Survival analysis for oncological patients * Planning of ideotypes of cereal plants to resist to climate changes * Mathematical and numerical modelling of cardiac electromechanical activity – Collaborations with industrial partners * Mathematical and computational models for Diffuse Optimal Tomography Requirements: Probability, Mathematical Statistics. Partial differential equations, analytical and numerical aspects. Differential Modelling | Aspri Andrea Causin Paola Cavaterra Cecilia Micheletti Alessandra Scacchi Simone |
| KAM and normal form methods for modulation equations and for the deduction of effective equations (non relativistic limit, equations for wave packets, many body equations in classical and quantum mechanics). PRIN project “Hamiltonian and Dispersive PDEs” Requirements: Elementary properties of Hamiltonian systems and partial differential equations | Bambusi Dario Paolo |
| Mathematical methods in quantum many body theory: emergent properties in Fermi gases (related to the ERC Starting Grant 2021 “FermiMath”) Requirements: Basic knowledge of functional analysis (Hilbert space theory, unbounded operators) | Benedikter Niels Patriz |
| Bosonization in dimensions 1+1 and 3+1 for interacting fermionic systems in scaling limits, ground state energy (related to the ERC Starting Grant 2021 “FermiMath”) Requirements: Basic knowledge of functional analysis (Hilbert space theory, unbounded operators) | Benedikter Niels Patriz |
| Semiclassical limits in quantum mechanics: quantitative analysis via Bogolioubov theory and normal forms (related to ERC Starting Grant 2021 “FermiMath” and ERC Starting Grant 2021 “HamDyWWa“) Requirements: Basic knowledges of quantum mechanics, perturbation theory, partial differential equations and functional analysis | Benedikter Niels Patriz Montalto Riccardo |
| Homotopical methods in arithmetic geometry Requirements: Commutative algebra, scheme theory and some background in homotopica/homological algebra | Binda Federico Vezzani Alberto |
| Rigid geometry, logarithmic geometry and perfectoid spaces Requirements: Number theory, algebraic geometry, commutative algebra and homological algebra | Binda Federico Vezzani Alberto |
| Mathematics learning environments in secondary school and integration of digital technologies for teaching Requirements: Knowledge of mathematics at university level relevant for teaching in upper secondary school. Elements of mathematics teaching | Branchetti Laura |
| Interdisciplinarity in the initial training of mathematics teachers Requirements: Knowledge of mathematics and physics or computer science at university level relevant for teaching in upper secondary school. Didactic elements of mathematics or physics or computer science | Branchetti Laura |
| Problems of learning and task design in the school-university transition Requirements: Knowledge of mathematics at university level relevant for teaching in upper secondary school. Elements of mathematics teaching | Branchetti Laura |
| Algebraic Geometry: projective models, automorphism groups and moduli spaces of Hyperkähler manifolds, irreducible symplectic varieties and Enriques varieties. Requirements: Good knowledge of algebraic geometry ad of complex geometry | Camere Chiara |
| Stochastic optimal control, backward stochastic differential equations and control of McKean-Vlasov systems. Requirements: Stochastic processes and stochastic calculus | Campi Luciano Cosso Andrea Fuhrman Marco Alessandro |
| Stochastic differential games and mean field games with applications Requirements: Stochastic processes and stochastic calculus | Campi Luciano |
| Spectral analysis of PDEs on manifolds Requirements: Basic understanding of PDEs, functional analysis and differential geometry | Capoferri Matteo |
| Spectral problems in the homogenization of PDEs with random coefficients Requirements: Basic understanding of PDEs, functional analysis and probability | Capoferri Matteo |
| Optimal Transport in Lorentzian manifolds. Structure of Lorentzian length spaces and synthetic curvature bounds Requirements: Basic knowledge of optimal transport and of differential geometry | Cavalletti Fabio |
| Mathematical modelling in Cultural Heritage Requirements: Good knowledge of basic mathematical analysis. Elements of real and functional analysis. | Cavaterra Cecilia Bonetti Elena |
| Evolution systems of partial differential equations and applications. Requirements: Good knowledge of basic mathematical analysis. Elements of real and functional analysis. | Cavaterra Cecilia Bonetti Elena |
| Inverse problems for systems of partial differential equations: identification of parameters, inclusions and inhomogeneities. Requirements: Good knowledge of basic mathematical analysis. Elements of real and functional analysis. | Cavaterra Cecilia Aspri Andrea |
| Geometric properties of solutions to partial differential equation Requirements: Knowledge of the basics of analysis and geometry, with emphasis in partial differential equations and basics of functional analysis | Ciraolo Giulio |
| Regularity for solutions to elliptic PDEs Requirements: Knowledge of the basics of analysis and geometry, with emphasis in partial differential equations and basics of functional analysis | Ciraolo Giulio |
| Hamilton-Jacobi-Bellman equations on Wasserstein spaces or function spaces Requirements: Stochastic processes and stochastic calculus | Cosso Andrea |
| Reinforcement learning in continuous time Requirements: Stochastic processes and stochastic calculus | Cosso Andrea |
| Foundational problems in Financial Mathematics: Fundamental Theorem of Asset Pricing with cooperating agents; martingale optimal transport; time consistency in the theory of preferences. Requirements: Good knowledge of functional analysis and of probability theory, in addition to the classical aspects of financial mathemtatics. | Frittelli Marco Maggis Marco |
| Varieties with trivial canoncial bundle: quotients, fibrations and Hodge structures Requirements: Basic notions in algebraic and complex geometry | Garbagnati Alice |
| Algebraic logic , categorical logic and duality theory, model-checking and decision procedures, non standard analysis and Ramsey theory Requirements: Good mathematical background, together with knowledge of fundamental mathematical logic results and techniques | Ghilardi Silvio Marra Vincenzo Luperi Baglini Lorenzo Reggio Luca Pasquali Fabio |
| Mathematical analysis of low-energy properties of quantum systems: homogeneous and non-homogeneous Fermi gases Requirements: Basic knowledge of functional analysis and quantum mechanics | Giacomelli Emanuela Laura |
| Analysis of effective models in superconductivity: Ginzburg-Landau theory and BCS theory Requirements: Basic knowledge of PDEs and functional analysis | Giacomelli Emanuela Laura |
| Classification of semi-discrete Hamiltonian systems Requirements: Basic knowledge of Hamiltonian mechanics in finite dimensions, differential and Riemannian geometry, projective geometry | Gubbiotti Giorgio |
| Integrable systems in N dimensions and generalisations Requirements: Basic knowledge of Hamiltonian mechanics in finite dimensions, differential and Riemannian geometry, projective geometry | Gubbiotti Giorgio |
| Geometry, dynamics, and symmetries of Bertini-Moody-Manin involutions Requirements: Basic knowledge of algebraic and complex geometry | Gubbiotti Giorgio |
| Classification on study of discrete-time systems admitting coalgebra symmetry Requirements: Basic knowledge of Lie algebras and dynamical systems | Gubbiotti Giorgio |
| Complexity and growth of birational maps of projective spaces in dimension higher than 2 Requirements: Basic knowledge of algebraic and complex geometry | Gubbiotti Giorgio |
| Algebraic geometry, derived categories, birational geometry. Part of the project Progetto PRIN 2020: Curves, Ricci flat varieties and their Interactions Requirements: Scheme theory, Riemann surfaces, homological algebra | Lombardi Luigi |
| Isogeometric analsysis and virtual element methods; numerical methods for partial differential equations. Project involved: PRIN 2020, Advanced polyhedral discretisations of heterogeneous PDEs for multiphysics problems Requirements: Numerical methods for partial differential equations | Lovadina Carlo Scacchi Simone |
| Existence, non-existence and rigidity results for submanifolds with prescribed curvature in Riemannian and Lorentzian ambient spaces. Requirements: Riemannian Geometry and PDE’s | Mari Luciano |
| Categorical Algebra Requirements: Basic knowledge of Category Theory, Universal and Homological Algebra | Mantovani Sandra Montoli Andrea |
| Computational geometry and topology for machine learning – research related with two industrial projects, with Dompé Farmaceutici, on problems of drug design, and with EDP Cnet on problems of segmentation of LiDAR images.A35:C35 Requirements: Real and functional analysis; topology; Statistics; neural networks | Micheletti Alessandra |
| Probabilistic and Statistical Methods for Forensic Anthropological Identification. The interdisciplinary research is caried out in collaboration with the Labanof (Laboratorio di Antropologia e Odontologia Forense – Sezione di Medicina Legale) in UNIMI. The research line is within the project FAITH – Fighting Against Injustice Through Humanities (strategic project of UNIMI) . Requirements: Mathematical statistics and probability theory | Micheletti Alessandra Morale Daniela Ugolini Stefania |
| Space-time stochastic processes, Stochastic Geometry and statistical shape analysis: point processes, random sets, random measures – research related with the morphological study of the skeleton of sea urchins for the planning of innovative bioinspired materials. In collaboration with the group of zoologists of the Department of Environmental Science and Policy Requirements: Measure theory; Probability and Mathematical Statistics | Micheletti Alessandra Villa Elena |
| Analytic Number Theory, with a special focus on explicit bounds and applications to algorithms computing algebraic invariants Requirements: Good knowledge of bases of Number theory, bot in analytic and algebraic flavours. | Molteni Giuseppe |
| Nonlinear waves in fluid mechanics and dispersive equations via quasi-linear Kam and normal form methods. ERC project: Hamiltonian Dynamics, Normal Forms and Water Waves Requirements: Basic knowledges of evolution PDEs, perturbation theory, Fourier and functional analysis | Montalto Riccardo |
| Stability of solitons and periodic and quasi-periodic waves for integrable and quasi-integrable Partial Differential equations – ERC project: Hamiltonian Dynamics, Normal Forms and Water Waves Requirements: Basic knowledges of evolution PDEs, integrable systems, perturbation theory, Fourier and functional analysis | Montalto Riccardo |
| Normal form methods for singular perturbation problems – ERC project: Hamiltonian Dynamics, Normal Forms and Water Waves Requirements: Basic knowledges of evolution PDEs, perturbation theory, Fourier and functional analysis | Montalto Riccardo |
| Statistical and stochastic analysis and calibration in modelling the degradation phenomenon in cultural heritages. SEED-UNIMI project and PON project on Green themes. The research is carried on in collaboration with the University of Pisa and University of Karlstad Requirements: Statistics, stochastic processes and stochastic calculus | Morale Daniela Ugolini Stefania |
| Limit behaviour of reaction diffusion partial differential equations with stochastic dynamical boundary condition. Randomness in front formation. Possible applications to the modelling of degradation phenomenon in cultural heritages. The research is carried on in collaboration with the University of Pisa, the University of Pavia and the Oslo University. Requirements: Stochastic processes and stochastic calculus | Morale Daniela Ugolini Stefania |
| Analysis of stochastic equations and interacting particles systems. Propagation to chaos: convergence problems from the nano to macroscale. Possible applicaion to the modelling of degradation phenomenon in cultural heritages. . The research is carried on in collaboration with the University of Pisa, University of Pavia , Oslo Univeristy and University of Karlstad. Requirements: Stochastic processes and stochastic calculus | Morale Daniela Ugolini Stefania |
| Motivic homotopy theory, motivic cohomology, motives, K-theory Requirements: Algebraic geometry and topology, homotopical algebra, infinity categories | Oestvaer Paul Arne |
| Harmonic Analysis, Complex Analysis Requirements: Basic knowledge of real, complex and functional analysis | Calzi Mattia Peloso Marco Maria |
| Stability conditions on triangulated categories and the geometry of moduli spaces Requirements: Solid background in complex algebraic geometry | Pertusi Laura |
| Differential Geometry and Global Analysis Requirements: Riemannian Geometry and PDE’s | M. Rigoli Mastrolia Paolo Mari Luciano |
| p-adic methods in arithmetic Requirements: Number Theory, Algebraic Geometry and Commutative Algebra | Seveso Marco Adamo Venerucci Rodolfo |
| Rational points on elliptic curves Requirements: Number Theory, Algebraic Geometry and Commutative Algebra | Seveso Marco Adamo Venerucci Rodolfo |
| Algebraic Geometry and Homological Algebra: derived, triangulated and dg categories in algebraic geometry Requirements: Solid background in algebraic geometry | Stellari Paolo |
| Geometric Analysis, Geometric Measure Theory and regularity of solutions to geometric variational problems (within project FIS 2 “Singularities in Geometric Analysis: Minimal Surfaces and Mean Curvature Flows (SiGmA)”) Requirements: Solid background in Mathematical Analysis and Measure Theory. Good knowledge of the main techniques in elliptic PDE theory and Calculus of Variations. Knowledge of Riemannian Geometry. Geometric intuition. | Stuvard Salvatore |
| Fine properties and regularity of weak solutions to Mean Curvature Flows (within project FIS 2 “Singularities in Geometric Analysis: Minimal Surfaces and Mean Curvature Flows (SiGmA)”) Requirements: Solid background in Mathematical Analysis and Measure Theory. Good knowledge of the main techniques in parabolic PDE theory. Knowledge of Riemannian Geometry. | Stuvard Salvatore |
| Birational geometry of algebraic foliations and their moduli spaces Requirements: Foundations of algebraic geometry and/or theory of holomorphic foliations. It may be beneficial to have at least a rudimentary knowledge of the Minimal Model Program and of moduli theory | Svaldi Roberto Tasin Luca |
| Boundedness problems in algebraic geometry Requirements: Foundations of algebraic geometry, particularly of Fano and/or Calabi–Yau varieties. It may be beneficial to have at least a rudimentary knowledge of the Minimal Model Program, | Svaldi Roberto Tasin Luca |
| Geometry of the moduli spaces of curves and higher dimensional varieties (of general type, Calabi-Yau or Fano Requirements: Foundations of algebraic geometry and basic knowledge on moduli theory | Svaldi Roberto Tasin Luca |
| Qualitative properties of nonlinear elliptic pdes and systems with critical variational growth. Sharp embedding inequalities for Sobolev type spaces, extremal functions and related phenomena. Requirements: Basic background in real analysis and functional analysis. Good knowledge of the main techniques in elliptic PDE theory and in variational methods. | Tarsi Cristina |
| Stochastic methods in quantum mechanics. The main research line is the stochastic description of the time-dependent Bose-Einstein condensation phenomenon. The research is carried on in collaboration with the University of Bonn, the University of Pavia and the University of Wuppertal. Requirements: Stochastic processes and stochastic calculus | Ugolini Stefania |
| Study of invariance and symmetry properties of stochastic dynamical systems, generalizing the classical theory of S. Lie. The research is carried on in collaboration with the University of Bonn and the University of Pavia. Requirements: Stochastic processes and stochastic calculus | Ugolini Stefania |
| Galerkin methods for partial differential equations. Project involved: PRIN 2020, Advanced polyhedral discretisations of heterogeneous PDEs for multiphysics problems Requirements: Theory and practice of Finite Element Methods; fundamentals of Numerical Linear Algebra | Veeser Andreas Lovadina Carlo |