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
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
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
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 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
Group Theory and Representation Theory
Requisiti: Basics in Algebra and Group Theory
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 infinite-dimensional convexity
Requisiti: Real analysis, Elements of Functional analysis

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 09/09/2020


Read the Call



Attachments and documents


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


Attachment 1