Research Lines 2022-23

TITLEREQUIREMENTSPROFESSOR/S
Study of stochastic partial differential equations. Field theory (stochastic quantization)Stochastic calculus, mathematical analysis of partial differential equationsAlbeverio S.
Normal forms and growth of Sobolev norms in Hamiltonian PDEs in more than higher space dimensionPerturbation theory for classical Hamiltonian systems, Birkhoff normal form, elements of functional analysisBambusi D. – Montalto R.
Energy sharing in multiparticle quantum systems, quantum Nekhoroshev’s theoremPerturbation theory for classical Hamiltonian systems, Birkhoff normal form, elements of functional analysisBambusi D. – Montalto R.
Normal form theory for quantum systems and validity in time of effective non-linear equations (connected to the ERC Starting Grants 2021 „FermiMath“ and „HamDyWWa“Hamiltonian mechanics, basic quantum theoryBambusi D. – N. Benedikter – Boccato C. – Montalto R.
Mathematical Methods in Many-Body Quantum Mechanics: emergent behavior in Fermi and Bose gases (connected to the ERC Starting Grant 2021 „FermiMath“)fundamentals of functional analysis (Hilbert space theory)Benedikter N. – Boccato C.
Bosonization in 1+1 and 3+1 dimensions for interacting fermionic systems in the scaling limit, ground state energy  and relation with Adler-Bardeen anomalies (connected to the ERC Starting Grant 2021 „FermiMath“)Knowledge of mathematical physics, analytical skills  Benedikter N. – Mastropietro V.
Group Theory and Representation TheoryBasic Algebra and Group TheoryBianchi M.
Homotopical methods in arithmetic geometryCommutative algebra, scheme theory and some background in homotopica/homological algebraBinda F. – Vezzani A.
Rigid geometry, logarithmic geometry and perfectoid spacesNumber theory, algebraic geometry, commutative algebra and homological algebraBinda F. – Vezzani A.
Mathematics learning environments in secondary school and integration of digital technologies for teachingKnowledge of mathematics at university level relevant for teaching in upper secondary school. Elements of mathematics teachingBranchetti L.
Interdisciplinarity in the initial training of mathematics teachersKnowledge 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 scienceBranchetti L.
Problems of learning and task design in the school-university transitionKnowledge of mathematics at university level relevant for teaching in upper secondary school. Elements of mathematics teachingBranchetti L.
Integrodifferential equations and nonlocal minimal surfacesGood knowledge of partial differential equations and of the basics of geometryBucur C. – Cozzi M.
Mean Field Games and applications in Mathematical FinanceStochastic optimal control, Probability, Stochastic CalculusBurzoni M.
Algebraic Geometry: projective models, automorphism groups and moduli spaces of Hyperkähler manifolds, irreducible symplectic varieties and Enriques varieties. This project is part of the project PRIN2020 “Curves, Ricci flat varieties and their interactions”.Good knowledge of algebraic geometry ad of complex geometryCamere C.
Stochastic differential games and mean field games with applicationsStochastic processes, stochastic calculusCampi L.
Stochastic optimal control, backward stochastic differential equations and control of systems of McKean-Vlasov type.Stochastic processes; stochastic calculus.Campi L. – Fuhrman M.
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
Probability, Mathematical Statistics. Partial differential equations, analytical and numerical aspects. Differential Modelling. Causin P. – Cavaterra C. – Micheletti A. – Scacchi S.
Inverse problems for systems of partial differential equations: identification of parameters, inclusions and inhomogeneities.Good knowledge of basic mathematical analysis. Elements of real and functional analysis.Cavaterra C.
Mathematical modelling in applications: Research line connected with project SCICULT- Bando SEEDS-SOE Unimi.Good knowledge of basic mathematical analysis. Elements of real and functional analysis.Cavaterra C. – Bonetti E.
Evolution systems of partial differential equations and applications. Research line connected with project PRIN 2020: Mathematics for industry 4.0 (Math4I4).Good knowledge of basic mathematical analysis. Elements of real and functional analysis.Cavaterra C. – Bonetti E.
Geometric properties of solutions to partial differential equationKnowledge of the basics of analysis and geometry, with emphasis in partial differential equations and basics of functional analysisCiraolo G.
Optimal Transport, Martingales and financial mathematicsFunctional Analysis, convex analysis, measure theory and stochastic processFrittelli M.
Financial MathematicsFunctional analysis,  probability and stochastic processFrittelli M.
Stochastic differential equationsStochastic processes; stochastic calculusFuhrman M.
Varieties with trivial canonical bundle: quotients, fibrations and Hodge structures- part of the Prin project “Curves, Ricci flat varieties and their interactions”Basic notions in algebraic and complex geometryGarbagnati A.
Algebraic logic and duality theory, model-checking and decision procedures, nonstandard analysis and Ramsey theoryGood general mathematical backgroundGhilardi S. – Marra V.
Algebraic Geometry; Derived categories of sheavesAlgebraic geometry, scheme theory, complex manifoldsLombardi L.
Isogeometric analsysis and virtual element methods; numerical methods for partial differential equations. Projects involved: PRIN 2017, Virtual Element Methods: Analysis and Applications; PRIN 2020, Advanced polyhedral discretisations of heterogeneous PDEs for multiphysics problemsNumerical methods for partial differential equationsLovadina C. – Scacchi S.
 Ambiguity in financial mathematics and economicsFunctional analysis,  measure theory and stochastic processMaggis M. – Burzoni M.
Categorical AlgebraBasic knowledge of Category Theory, Universal and Homological AlgebraMantovani S. – Montoli A.
Conoscenze di base di fisica matematica, analisi e probablità; interesse per la fisica modernaBasic knowledge of mathematical physics, analysis and probability.Mastropietro V.
Computational geometry and topology for machine learning – research related with the Italian PNRR thematic ‘Artificial intelligence: foundational aspects’ and to the industrial project “Development of methods of computational topology and explainable machine learning applied to molecular docking”Real and functional analysis; topology; Statistics; neural networksMicheletti A.
Space-time stochastic processes, Stochastic Geometry and statistical shape analysis: point processes, random sets, random measures – research related with the ECMI Special Interest group “Shape and size in medicine, biotechnology and materials science”Measure theory; Probability and Mathematical StatisticsMicheletti A. – Villa E.
normal form methods for singular perturbation problems – ERC project: : Hamiltonian Dynamics, Normal Forms and Water WavesHamiltonian systems and basic normal form theory. Elementary knowledge of Fourier Analysis and partial differential equationsMontalto R.
stability of periodic multi-solitons and perturbations of nonlinear integrable systems – ERC project: : Hamiltonian Dynamics, Normal Forms and Water WavesHamiltonian systems and basic normal form theory. Elementary knowledge of Fourier Analysis and partial differential equations. Elementary knowledge on the theory of integrable systemsMontalto R.
kam and normal form methods for pdeS in fluid dynamics – ERC project: : Hamiltonian Dynamics, Normal Forms and Water WavesHamiltonian systems and basic normal form theory. Elementary knowledge of Fourier Analysis and partial differential equationsMontalto R. – Bambusi D.
Computational statistical and stochastic analysis in the framework of the modelling of phenomena such as the degradation of cultural heritage, energy markets and so on

The research line is  of modellistic and applicative nature, connected to both the SEED-UNIMI SCICULT project and to a PON research project on Green themes, under the supervision of the proposers and to current research lines. Possible collaboration  with researchers of the CNR, the university of Pisa and Karlsdadt (Sweden)
Stochastic calculus, statistics, numerical methods for PDEMorale D. – Ugolini S.
Analysis of stochastic and deterministic differential equations, boundary problems and interacting particle system for the modelling connected to problems of climate  and environmental changes and the degradation of cultural heritage.  

The research line is  of modellistic and analitic nature, connected to both the SEED-UNIMI SCICULT project and to a PON research project on Green themes, under the supervision of the proposers and to current research lines. Possible collaboration  with researcher of the CNR, the university of Pisa and Karlsdadt (Sweden)
Analutical skills, knowledge of deterministic differential equations, stochastic calculusMorale D. – Ugolini S.
Motivic homotopy theory, motivic cohomology, motives, K-theoryAlgebraic geometry and topology, homotopical algebra, infinity categoriesOestvaer P. A.
(Perturbation theory for) finite dimensional Hamiltonian systems and application to the dynamics of non linear latticesKnowledge of mathematical physics and basic elements of Hamiltonian dynamical systemsPaleari  S. – Penati T.
Mathematical Methods in Quantum Mechanics and in General Relativity; Evolution equations (especially, in fluid dynamics) .                                 The proponent is financially supported by:                                1) MIUR, Project PRIN 2020 ”Hamiltonian and dispersive PDEs”;
2) Università degli Studi di Milano, PSR2021, Project
”Classical and quantum dynamical systems, statistical mechanics”;
3) Istituto Nazionale di Fisica Nucleare, Specific Initiative BELL  
Basic knowledge of functional analysis and quantum mechanics;
Basic knowledge of differential geometry and general relativity
Pizzocchero L.
Epistemology of MathematicsGood knowledge of geometry, analysis,…and of the philosophical aspects of the theory of knowledgeRigoli M.
Differential Geometry and Global AnalysisRiemannian Geometry and PDE’sRigoli M. – Mastrolia P.
Study of p-adic L-functions and p-adic regulators with applications to the arithmetic of automorphic formsKnowledge of basic number theory and modular formsSeveso M.
Algebraic Geometry and Homological AlgebraSlid background in algebraic geometryStellari P.
Geometric Measure Theory and regularity of solutions to geometric variational problemsSolid background in Mathematical Analysis and Measure Theory. Knowledge of the main techniques in elliptic PDE and Calculus of Variations. Geometric intuitionStuvard S. – Ciraolo G.
Fine properties and regularity of weak solutions to Mean Curvature FlowsSolid background in Mathematical Analysis and Measure Theory. Basic knowledge of the geometry of hypersurfaces. Knowledge of the main techniques in parabolic PDEStuvard S. – Ciraolo G.
Birational geometry of the moduli space of curves: MMP and Hassett-Keel programGood knowledge of algebraic geometry. Basic notions of moduli spacesTasin L.
Stochastic methods in quantum mechanics: stochastic description of the quantum phenomenon of Bose-Einstein condensation. Scaling, convergence and an approach via stochastic optimal control. Research line is carried out in collaboration with the University of Bonn (HCM)Stochastic calculus, mathematical analysisUgolini S. – Albeverio S.
Study of invariance and symmetry properties of stochastic dynamical systems. The research is carried out in collaboration with the University of Bonn (HCM)Stochastic calculus, mathematical analysisUgolini S. – Albeverio S.
Non-local Problems and Free boundary problemsAdvance skills in mathematical analysisValdinoci E.
Nonlocal minimal surfacesKnowledge of the basics of analysis and geometry. Geometric intuition and knowledge of partial differential equationsValdinoci E.
Phase coexistence problemsKnowledge of the basics of analysis and mathematical physics, with emphasis in partial differential equations.Valdinoci E.
Algebraic geometry and Hodge theory (PRIN)Basic knowledge of algebraic and complex  geometryvan Geemen B.
Foundations of adaptive methods for the numerical solution of differential equations. Involved projects: PRIN 2017, Numerical Analysis for Full and Reduced Order Methods for the efficient and accurate solution of complex systems governed by Partial
Differential Equations
Sound knowledge of conforming and non-conforming Galerkin methods, in particular finite element methods; basic knowledge of nonlinear approximationVeeser A.
Galerkin methods for partial differential equations. Projects involved: PRIN 2017, Virtual Element Methods: Analysis and Applications; PRIN 2017, Numerical Analysis for Full and Reduced Order Methods for the efficient
and accurate solution of complex systems governed by Partial Differential Equations; PRIN 2020, Advanced polyhedral discretisations of heterogeneous PDEs for multiphysics problems 
Theory and practice of Finite Element Methods; fundamentals of Numerical Linear AlgebraVeeser A. – Lovadina C.