Mathematical sciences

Dottorati
Doctoral programme (PhD)
A.Y. 2020/2021
Study area
Science and Technology
Doctoral programme (PhD)
3
Years
Dip. Matematica 'Federigo Enriques' - Via Saldini, 50 - Milano
Italian
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 three-year 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
Title Professor(s)
Space-time 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: Sound 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
Stochastic optimal control
Requirements: Stochastic processes. Stochastic calculus
p-adic modular forms and L-functions, algebraic cycles, motives and their realizations
Requirements: Theory of schemes, number theory and homological algebra
Mathematical logic, algebraic logic, duality theory, model-checking 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
Non-local 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 Calabi-Yau 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
Stochastic differential equations
Requirements: Stochastic Calculus
Inverse problems for partial differential equations
Requirements: Basic knowledge of Real and Functional Analysis
L. Rondi
Variational methods for imaging and for shape optimization
Requirements: Basic knowledge of Real and Functional Analysis
L. Rondi
Group Theory and Representation Theory
Requirements: Basics in Algebra and Group Theory
E. Pacifici
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 infinite-dimensional convexity
Requirements: 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

Read the Call


Attachments and documents

Assessment criteria and results of the assessment of the qualifications and information about the oral exam

Attachment 1