Research Lines 2021-22

Space-time stochastic processes, Stochastic geometry and statistical shape analysis: point processes, random sets, random measuresMeasure theory; Probability and Mathematical Statistics E. Villa; A. Micheletti 
Biomathematics and BiostatisticsProbability, Mathematical Statistics. Partial differential equations, analytical and numerical aspects. Differential Modelling.  C. Cavaterra; A. Micheletti 
Categorical algebraBasic knowledge of Category Theory, Universal and Homological AlgebraS. Mantovani; A. Montoli 
Stochastic methods in quantum mechanicsStochastic calculus and analytical skillsS. Albeverio; S. Ugolini 
Invariance properties in stochastic dynamicsStochastic calculus and analytical skillsS. Albeverio; S. Ugolini 
Stochastic partial differential equations and quantum field theoryStochastic calculus and analytical skillsS. Albeverio
Foundations of adaptive methods for the solution of differential equationsSound knowledge of Galerkin methods with conforming and nonconforming spaces, basic knowledge of nonlinear approximationA. Veeser 
Numerical Galerkin methods for partial differential equationsTheory and practice of finite element methods, numerical linear algebraA. Veeser; C. Lovadina

Algebraic Geometry and Homological AlgebraSlid background in algebraic geometryP. Stellari
p-adic modular forms and L-functions, algebraic cycles, motives and
their realizations
Theory of schemes, number theory and homological algebraF. Andreatta 
Mathematical logic, algebraic logic, duality theory, model-checking and decision procedures.Good general mathematical backgroundS. Ghilardi; V. Marra 
Isogeometric Analysis and Virtual Element Method; Numerical methods for partial differential equations; BiomathematicsNumerical Methods for PDEsC. Lovadina; S. Scacchi 
Non-local Problems and Free boundary problemsAdvance skills in mathematical analysisE. Valdinoci 
Nonlocal minimal surfacesKnowledge of the basics of analysis and geometry. Geometric intuition and knowledge of partial differential equationsE. Valdinoci 
Phase coexistence problemsKnowledge of the basics of analysis and mathematical physics, with emphasis in partial differential equations.E. Valdinoci
Evolution systems of PDEReal analysis, functional analysisE. Bonetti; C. Cavaterra 
Mathematical models for applicationsReal analysis, functional analysisE. Bonetti; C. Cavaterra 
Inverse problemsReal analysis, functional analysisE. Bonetti; C. Cavaterra 
Differential Geometry and Global AnalysisRiemannian Geometry and PDE’sM. Rigoli; P. Mastrolia 
Epistemology of MathematicsGood knowledge of geometry, analysis,…and of the philosophical aspects of the theory of knowledgeM. Rigoli 
Mathematical Physics for quantum and classical statistical mechanics and quantum field theoryKnowledge of mathematical physics, analytical skills  V. Mastropietro 
Mathematical Methods in Quantum Mechanics and in General Relativity; Evolution equations (especially, in fluid dynamics)Basic knowledge of functional analysis and quantum mechanics; Basic knowledge of differential geometry and general relativityL. Pizzocchero 
Non linear Analysis, nonlinear partial differential equationsBasic knowledge of Functional analysis, PDEs and Sobolev spaces B. Ruf 
Algebraic geometry and Hodge theory, Moduli spaces of curves and  Geometry of Calabi-Yau varieties Basic knowledge of algebraic and complex  geometryL. van Geemen 
Non linear DynamicsElementary techniques of dynamic systemsD. Bambusi 
KAM and normal form theory for PDEsBasic elements of Hamiltonian systemsD. Bambusi 
Group Theory and Representation TheoryBasics in Algebra and Group TheoryM. Bianchi 
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 analysis.G. Ciraolo 
Finite dimensional Hamiltonian dynamics: from nonlinear chains to celestial mechanicsKnowledge of mathematical physics and basic elements of Hamiltonian dynamical systemsM. Sansottera; T. Penati; S. Paleari  
Financial MathematicsFunctional analysis, probability and stochastic processesM. Frittelli 
Ambiguity modelling in mathematical financeFunctional analysis, measure theory, stochastic calculusM. Maggis; M. Burzoni 
Martingale Optimal Transport and Financial mathematics Functional analysis, convex analysis, measure theory, stochastic calculusM. Frittelli
Functional analysis and infinite-dimensional convexityReal analysis, Elements of Functional analysisL. Vesely 
kam and normal form methods for pdeS in fluid dynamicsHamiltonian systems and basic normal form theory. Elementary knowledge of Fourier Analysis and partial differential equationsR. Montalto
normal form methods for singular perturbation problemsHamiltonian systems and basic normal form theory. Elementary knowledge of Fourier Analysis and partial differential equationsR. Montalto
stability of periodic multi-solitons and perturbations of nonlinear integrable systemsHamiltonian systems and basic normal form theory. Elementary knowledge of Fourier Analysis and partial differential equations. Elementary knowledge on the theory of integrable systemsR. Montalto
Stochastic optimal control, backward stochastic differential equations and control of systems of McKean-Vlasov type.Stochastic processes; stochastic calculus.L. Campi; M. Fuhrman 
Stochastic differential equations.Stochastic processes; stochastic calculus.M. Fuhrman 
Algebraic geometry: geometry, automorphisms and constructions of varieties with trivial canonical bundles and with elliptic fibrationsBasic knowledge of algebraic and complex geometry A. Garbagnati
Computational topology for machine learningReal and functional analysis; topology; Statistics; neural networksA. Micheletti 
Stochastic differential games and mean field games with applicationsStochastic processes, stochastic calculusL. Campi 
Algebraic Geometry: projective models, automorphism groups and moduli spaces of Hyperk√§hler manifolds and irreducible symplectic varieties.Good knowledge of algebraic geometry ad of complex geometryC. Camere