Mathematical sciences

Dottorati
Doctoral programme (PhD)
A.Y. 2019/2020
Study area
Science and Technology
Doctoral programme (PhD)
3
Years
Dip. Matematica 'Federigo Enriques' - Via Saldini, 50 - Milano
Italian
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.
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
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: Slid background in algebraic geometry
Stochastic optimal control
Requisiti: Stochastic processes. Stochastic calculus
p-adic modular forms and L-functions, algebraic cycles, motives and their realizations
Requisiti: Theory of schemes, number theory and homological algebra
Mathematical logic, algebraic logic, duality theory, model-checking 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
Non-local 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
Mathematical Physics for quantum and classical statistical mechanics and quantum field theory
Requisiti: Knowledge of mathematical physics, analytical skills
Financial Mathematics
Requisiti: Functional analysis, Probability and stochastic processes
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 Calabi-Yau 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
Variational methods for imaging and for shape optimization
Requisiti: Basic knowledge of Real and Functional Analysis

Courses list

January
Courses or activities Professor(s) ECTS Total hours Language
Categorical Methods in Algebra and Topology
3 16 English
March
Courses or activities Professor(s) ECTS Total hours Language
Dynamics of Hamiltonian PDEs: reducibility and growth of sobolev norms 4 20 English
Miscellanea on complex projective varieties 3 15 English
April
Courses or activities Professor(s) ECTS Total hours Language
Quantum Many Body systems; time evolution and ground state energy
3 15 English
May
Courses or activities Professor(s) ECTS Total hours Language
Regularization by noise 3 15 English
July
Courses or activities Professor(s) ECTS Total hours Language
Classical and fractional partial differential equations under different perspectives
Valdinoci Enrico
5 25 English

Enrollment

Places available: 8


Call for applications: how to do, attachment 1


Application period: from 05-24-2019 to 06-24-2019
Enrolment period: from 09-23-2019 to 09-27-2019