Research Lines 2020-21 – University of Milan

Title	Requirements	Professor/s
Stochastic partial differential equations and quantum field theory	Stochastic calculus and analytical skills	Albeverio S.
Stochastic methods in quantum mechanics	Stochastic calculus and analytical skills	Albeverio S. Ugolini S.
Invariance properties in stochastic dynamics	Stochastic calculus and analytical skills	Albeverio S. Ugolini S.
p-adic modular forms and L-functions, algebraic cycles, motives and their realizations	Theory of schemes, number theory and homological algebra	Andreatta F.
Non linear Dynamics	Elementary techniques of dynamic systems	Bambusi D.
KAM and normal form theory for PDEs	Basic elements of Hamiltonian systems	Bambusi D.
Inverse problems	Real analysis, functional analysis	Bonetti E. Cavaterra C.
Evolution systems of PDE	Real analysis, functional analysis	Bonetti E. Cavaterra C.
Mathematical models for applications	Real analysis, functional analysis	Bonetti E. Cavaterra C.
Ambiguity modelling in mathematical finance	Functional analysis, measure theory, stochastic calculus	Burzoni M. Maggis M.
Space-time stochastic processes, Stochastic geometry and statistical shape analysis: point processes, random sets, random measures	Measure theory; Probability and Mathematical Statistics	Cavaterra C. Micheletti A.
Biomathematics and Biostatistics	Probability, Mathematical Statistics. Partial differential equations, analytical and numerical aspects. Differential Modelling.	Cavaterra C. Micheletti A.
Geometric properties of solutions to partial differential equation	Knowledge of the basics of analysis and geometry, with emphasis in partial differential equations and basics of functional analysis.	Ciraolo G.
Financial Mathematics	Functional analysis, probability and stochastic processes	Frittelli M.
Martingale Optimal Transport and Financial mathematics	Functional analysis, convex analysis, measure theory, stochastic calculus	Frittelli M.
Stochastic optimal control	Stochastic processes. Stochastic calculus	Fuhrman M.
Stochastic differential equations.	Stochastic Calculus	Fuhrman M.
Mathematical logic, algebraic logic, duality theory, model-checking and decision procedures.	Good general mathematical background	Ghilardi S. Marra V.
Isogeometric Analysis and Virtual Element Method; Numerical methods for partial differential equations; Biomathematics	Numerical Methods for PDEs	Lovadina C. Scacchi S.
Numerical Galerkin methods for partial differential equations	Theory and practice of finite element methods, numerical linear algebra	Lovadina C. Veeser A.
Categorical algebra	Basic knowledge of Category Theory, Universal and Homological Algebra	Mantovani S. Montoli A.
Differential Geometry and Global Analysis	Riemannian Geometry and PDE’s	Mastrolia P. Rigoli M.
Mathematical Physics for quantum and classical statistical mechanics and quantum field theory	Knowledge of mathematical physics, analytical skills	Mastropietro V.
Group Theory and Representation Theory	Basics in Algebra and Group Theory	Pacifici E.
Finite dimensional Hamiltonian dynamics: from nonlinear chains to celestial mechanics	Knowledge of mathematical physics and basic elements of Hamiltonian dynamical systems	Paleari S. Penati T. Sansottera M.
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 relativity	Pizzocchero L.
Epistemology of Mathematics	Good knowledge of geometry, analysis,…and of the philosophical aspects of the theory of knowledge	Rigoli M.
Inverse problems for partial differential equations	Basic knowledge of Real and Functional Analysis	Rondi L.
Variational methods for imaging and for shape optimization	Basic knowledge of Real and Functional Analysis	Rondi L.
Non linear Analysis, nonlinear partial differential equations	Basic knowledge of Functional analysis, PDEs and Sobolev spaces	Ruf B.
Algebraic Geometry and Homological Algebra	Slid background in algebraic geometry	Stellari P.
Non-local Problems and Free boundary problems	Advance skills in mathematical analysis	Valdinoci E.
Nonlocal minimal surfaces	Knowledge of the basics of analysis and geometry. Geometric intuition and knowledge of partial differential equations	Valdinoci E.
Phase coexistence problems	Knowledge of the basics of analysis and mathematical physics, with emphasis in partial differential equations.	Valdinoci E.
Algebraic geometry and Hodge theory, Moduli spaces of curves and Geometry of Calabi-Yau varieties	Basic knowledge of algebraic and complex geometry	van Geemen L.
Foundations of adaptive methods for the solution of differential equations	Sound knowledge of Galerkin methods with conforming and nonconforming spaces, basic knowledge of nonlinear approximation	Veeser A.
Functional analysis and infinite-dimensional convexity	Real analysis, Elements of Functional analysis	Vesely L.