Mathematical sciences
Doctoral programme (PhD)
A.Y. 2021/2022
Study area
Science and Technology
PhD Coordinator
The doctoral programme in Mathematical Sciences aims to teach students the research techniques and methods typical of the sectors of contemporary Mathematics and their applications, both qualitative and quantitative, so as to obtain the wide ranging scientific and cultural autonomy required to produce original and significant results. The programme will produce graduates with expertise in exploiting the full potential of mathematical tools and methods and statistics to tackle the intrinsic complexity of problems posed by the applied sciences and industry. The first year syllabus includes advanced theory and workshops held by international scholars chosen by the Board of Lecturers to offer students the opportunity to establish direct contacts with the international scientific community. Doctoral students will have personalised courses under the guidance of a tutor. Once mandatory attendance of courses and examinations are completed, students can concentrate on their chosen research project. Students are assessed on the basis of their doctoral thesis, to which the threeyear doctoral programme dedicates considerable attention.
Tutte le classi di laurea magistrale  All classes of master's degree
Dip. Matematica 'Federigo Enriques'  Via Saldini, 50  Milano
 Main offices
Dip. Matematica 'Federigo Enriques'  Via Saldini, 50  Milano  Degree course coordinator: Vieri Mastropietro
vieri.mastropietro@unimi.it  Degree course website
http://www.mat.unimi.it/dottorati
Title  Professor(s) 

Spacetime stochastic processes, Stochastic geometry and statistical shape analysis: point processes, random sets, random measures.
Requirements: Measure theory; Probability and Mathematical Statistics. 

Biomathematics and Biostatistics
Requirements: Probability, Mathematical Statistics. Partial differential equations, analytical and numerical aspects. Differential Modelling. 

Categorical algebra
Requirements: Basic knowledge of Category Theory, Universal and Homological Algebra 

Stochastic methods in quantum mechanics
Requirements: Stochastic calculus and analytical skills 
S. Albeverio

Invariance properties in stochastic dynamics
Requirements: Stochastic calculus and analytical skills 
S. Albeverio

Stochastic partial differential equations and quantum field theory
Requirements: Stochastic calculus and analytical skills 
S. Albeverio

Foundations of adaptive methods for the solution of differential equations
Requirements: Solid knowledge of Galerkin methods with conforming and nonconforming spaces, basic knowledge of nonlinear approximation 

Numerical Galerkin methods for partial differential equations
Requirements: Theory and practice of finite element methods, numerical linear algebra 

Algebraic Geometry and Homological Algebra
Requirements: Solid background in algebraic geometry 

padic modular forms and Lfunctions, algebraic cycles, motives and their realizations
Requirements: Theory of schemes, number theory and homological algebra. 

Mathematical logic, algebraic logic, duality theory, modelchecking and decision procedures.
Requirements: Good general mathematical background 

Isogeometric Analysis and Virtual Element Method; Numerical methods for partial differential equations; Biomathematics
Requirements: Numerical Methods for PDEs 

Nonlocal Problems and Free boundary problems
Requirements: Advance skills in mathematical analysis 
E. Valdinoci

Nonlocal minimal surfaces
Requirements: Knowledge of the basics of analysis and geometry. Geometric intuition and knowledge of partial differential equations 
E. Valdinoci

Phase coexistence problems
Requirements: Knowledge of the basics of analysis and mathematical physics, with emphasis in partial differential equations. 
E. Valdinoci

Evolution systems of PDE
Requirements: Real analysis, functional analysis 

Mathematical models for applications
Requirements: Real analysis, functional analysis 

Inverse problems
Requirements: Real analysis, functional analysis 

Differential Geometry and Global Analysis
Requirements: Riemannian Geometry and PDE's 

Epistemology of Mathematics
Requirements: Good knowledge of geometry, analysis, and of the philosophical aspects of the theory of knowledge 

Mathematical Physics for quantum and classical statistical mechanics and quantum field theory
Requirements: Knowledge of mathematical physics, analytical skills 

Mathematical Methods in Quantum Mechanics and in General Relativity; Evolution equations (especially, in fluid dynamics)
Requirements: Basic knowledge of functional analysis and quantum mechanics; Basic knowledge of differential geometry and general relativity. 

Non linear Analysis, nonlinear partial differential equations
Requirements: Basic knowledge of Functional analysis, PDEs and Sobolev spaces 

Algebraic geometry and Hodge theory, Moduli spaces of curves and Geometry of CalabiYau varieties
Requirements: Basic knowledge of algebraic and complex geometry 

Non linear Dynamics
Requirements: Elementary techniques of dynamic systems 

KAM and normal form theory for PDEs
Requirements: Basic elements of Hamiltonian systems 

Group Theory and Representation Theory
Requirements: Basics in Algebra and Group Theory 

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. 

Finite dimensional Hamiltonian dynamics: from nonlinear chains to celestial mechanics
Requirements: Knowledge of mathematical physics and basic elements of Hamiltonian dynamical systems 

Financial Mathematics
Requirements: Functional analysis, probability and stochastic processes 

Ambiguity modelling in mathematical finance
Requirements: Functional analysis, measure theory, stochastic calculus 

Martingale Optimal Transport and Financial mathematics
Requirements: Functional analysis, convex analysis, measure theory, stochastic calculus 

Functional analysis and infinitedimensional convexity
Requirements: Real analysis, Elements of Functional analysis 

Kam and normal form methods for pdeS in fluid dynamics
Requirements: Hamiltonian systems and basic normal form theory. Elementary knowledge of Fourier Analysis and partial differential equations 

Normal form methods for singular perturbation problems
Requirements: Hamiltonian systems and basic normal form theory. Elementary knowledge of Fourier Analysis and partial differential equations 

Stability of periodic multisolitons and perturbations of nonlinear integrable systems
Requirements: Hamiltonian systems and basic normal form theory. Elementary knowledge of Fourier Analysis and partial differential equations. Elementary knowledge on the theory of integrable systems. 

Stochastic optimal control, backward stochastic differential equations and control of systems of McKeanVlasov type.
Requirements: Stochastic processes; stochastic calculus. 

Stochastic differential equations.
Requirements: Stochastic processes; stochastic calculus. 

Algebraic geometry: geometry, automorphisms and constructions of varieties with trivial canonical bundles and with elliptic fibrations.
Requirements: Basic knowledge of algebraic and complex geometry 

Computational topology for machine learning
Requirements: Real and functional analysis; topology; Statistics; neural networks. 

Stochastic differential games and mean field games with applications
Requirements: Stochastic processes, stochastic calculus. 

Algebraic Geometry: projective models, automorphism groups and moduli spaces of Hyperkähler manifolds and irreducible symplectic varieties.
Requirements: Good knowledge of algebraic geometry ad of complex geometry 
Courses list
Courses or activities  Professor(s)  ECTS  Total hours  Language 

Optional  
A tour on Kirchhoff type Problems  3  15  English  
Analytical aspects of local and nonlocal minimal surfaces  4  20  English  
Matematics for Statistical Physics and Quantum Field Theory  5  25  English  
Periods and period domains  4  20  Italian  
Population Genetics and Evolution  2  10  Italian  
Stochastic quantization of the Euclidean quantum field theory  4  20  English 
Enrollment
Places available: 8
Call for applications
Please refer to the call for admission test dates and contents, and how to register.
Application for admission: from 28/05/2021 to 28/06/2021
Application for matriculation: from 26/07/2021 to 30/07/2021
Attachments and documents
Following the programme of study
Contacts
Office and services for PhD students and companies