Mathematics

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Academic year 2022/2023
Faculty of Sciences
Scuola Normale Superiore di Pisa
EQF level: 8
38° cicle
Field of study: natural sciences, mathematics, physics and statistics
Place of teaching
pisa (PI), italy
Attendance methods
Full time
Languages in which the course is held
English, Italian
Cost
Free course
Scholarships
6 
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Course contents

Mathematics is the oldest science, and still one of the most important and widely applicable. The mathematical tradition at the Scuola Normale is quite strong, and our PhD program prepares high-level researchers, who routinely go on to teach and do research in very prestigious institutions, in Italy and abroad. Although our program is mostly in pure mathematics, the preparation that one obtains can easily be put to use in a vast range of fields with high scientific and technological content.
One of the characteristics of the Scuola Normale is the constant flow of visitors and post-docs from all over the world; this, together with the financial support offered to our students for visits to research institutes and universities of very high standing, greatly enlarges their research horizons. Also, its limited size favors interaction among students in different disciplines, resulting in a remarkable cultural and personal enrichment.
The mathematical research at the Scuola Normale is concentrated in some of the most significant areas of mathematics at the international level.
• In calculus of variations, our main activity is in geometric measure theory, even in metric measure spaces, elliptic and parabolic partial differential equations, optimal mass transport and its applications.
• In harmonic analysis the main themes are invariant operators on Lie Groups, singular integrals, Fourier multipliers, and Radon transforms. Methods of commutative and noncommutative harmonic analysis are also applied to complex analysis.
• In differential geometry and global analysis we treat non-linear problems in riemannian geometry and geometric evolutions, riemannian manifolds with special structures, such as solitons of the Ricci flow or quasi-Einstein manifolds, calibrated geometries and varieties with special holonomy, and the geometry of submanifolds.
• In probability and stochastic analysis we investigate stochastic partial differential equations, particle systems and scaling limits, Kolmogorov and Fokker-Planck equations, applications in turbulence and geophysics.
• In algebraic geometry we do research on algebraic stacks, essential dimension, actions of algebraic groups and their invariants, derived categories and toric varieties.
• In number theory the most studied aspects are the applications of geometric methods to the problems of integral points, with particular stress on the effectivity of solutions, heights, and intersection problems in algebraic groups.
• In dynamical systems we concentrate on problems of stability of quasi-periodic orbits, on KAM theory, on holomorphic dynamics, on the ergodic theory of continued fractions and on Teichmüller flows.
• In numerical analysis and scientific computing our main research interests are in numerical linear algebra, especially sparse matrix algorithms, iterative methods, preconditioning, and functions of matrices. Our activities range from theoretical foundations to algorithm development with applications to fluid mechanics, network science and quantum chemistry.
Page of the course on the University's website

Teaching

Place of teaching
pisa (PI), italy
Number of hours
150 ( 150 hours of learning activities)
Attendance methods
Full time
Compulsory attendance
Languages in which the course is held
English, Italian

Admission requirements

Type of degree required
2nd Level Degree
Field of study
natural sciences, mathematics, physics and statistics
Foreign language skills
English
Other educational requirements
a) were born after 31 October 1988;
b) have no past criminal charges against them resulting in a prison term of more than three years;
c) have not been subject to the disciplinary measure of “expulsion” as specified in the didactic regulations of the SNS;
d) are not in possession of a research doctorate issued by an Italian university, and in any case have never benefitted from a scholarship to attend a research doctorate course in Italy.

Admission

Available places
6
Admission
Admission selection
Academic assessment and interview
Cost
Free course
Scholarships
6

Employment opportunities

The most natural outcome of the doctorate is thevresearcher in mathematics in the academy, both in Italy and abroad.But the great flexibility that derives from a high level training in pure mathematics allows to adapt easily also to applied and industrial research environments, so the PhD students trained in the Scuola Normale will be able to find employment in research centers, for example, in cryptography and network security (which requires advanced knowledge of number theory), mathematical finance, weather forecasting, robotics, simulation of a large variety of physical, chemical and biological phenomena.In addition, our PhDs will certainly be able to fit into managerial positions, in industry, services and public administration, and occupy places where mathematicians are traditionally employed: software development, staff management in large companies, development and management of large databases, risk assessment for insurance companies, and many others.

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Other editions of the same course
Academic year edition 2021/2022Academic year edition 2020/2021Academic year edition 2019/2020

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