Mathematical sciences
Doctoral programme (PhD)
A.Y. 2020/2021
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
Requisiti: Measure theory; Probability and Mathematical Statistics 

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

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

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

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

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

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

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

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

Stochastic optimal control
Requisiti: Stochastic processes. Stochastic calculus 

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

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

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

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

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

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

Evolution systems of PDE
Requisiti: Real analysis, functional analysis 

Mathematical models for applications
Requisiti: Real analysis, functional analysis 

Inverse problems
Requisiti: Real analysis, functional analysis 

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

Epistemology of Mathematics
Requisiti: 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
Requisiti: Knowledge of mathematical physics, analytical skills 

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

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

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

Non linear Dynamics
Requisiti: Elementary techniques of dynamic systems 

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

Stochastic differential equations
Requisiti: Stochastic Calculus 

Inverse problems for partial differential equations
Requisiti: Basic knowledge of Real and Functional Analysis 
L. Rondi

Variational methods for imaging and for shape optimization
Requisiti: Basic knowledge of Real and Functional Analysis 
L. Rondi

Group Theory and Representation Theory
Requisiti: Basics in Algebra and Group Theory 
E. Pacifici

Geometric properties of solutions to partial differential equation
Requisiti: 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
Requisiti: Knowledge of mathematical physics and basic elements of Hamiltonian dynamical systems 

Financial Mathematics
Requisiti: Functional analysis, probability and stochastic processes 

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

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

Functional analysis and infinitedimensional convexity
Requisiti: Real analysis, Elements of Functional analysis 
Courses list
January 2021
Courses or activities  Professor(s)  ECTS  Total hours  Language 

Optional  
Matematics for Statistical Physics and Quantum Field Theory  5  25  English  
Periods and period domains  4  20  Italian 
February 2021
Courses or activities  Professor(s)  ECTS  Total hours  Language 

Optional  
Population Genetics and Evolution  2  10  Italian  
Stochastic quantization of the Euclidean quantum field theory  4  20  English 
March 2021
Courses or activities  Professor(s)  ECTS  Total hours  Language 

Optional  
Analytical aspects of local and nonlocal minimal surfaces  4  20  English 
April 2021
Courses or activities  Professor(s)  ECTS  Total hours  Language 

Optional  
A tour on Kirchhoff type Problems  3  15  English 
Enrollment
Places available: 7
Call for applications
Please refer to the call for admission test dates and contents, and how to register.
Application for admission: from 22/06/2020 to 22/07/2020
Application for matriculation: from 03/09/2020 to 02/11/2020
Attachments and documents
Following the programme of study
Contacts
Office and services for PhD students and companies