**Other program opportunities in Europe**

## 4 Results in Mathematics, Italy

The Ph.D. program in Geometry and Mathematical Physics focuses on the study of analytic and geometric aspects of physical phenomena that are of fundamental interest in bo ... [+]

The Ph.D. program in Geometry and Mathematical Physics focuses on the study of analytic and geometric aspects of physical phenomena that are of fundamental interest in both pure and applied sciences and covers a wide spectrum of topics in modern algebraic and differential geometry and their applications.

Research Topics Integrable systems in relation to differential, algebraic and symplectic geometry, as well as with the theory of random matrices, special functions and nonlinear waves, Frobenius manifolds Deformation theory and virtual classes moduli spaces of sheaves and of curves, in relation to supersymmetric gauge theories, strings, Gromov-Witten invariants, orbifolds and automorphisms Quantum groups, noncommutative Riemannian and spin geometry, applications to models in mathematical physics Mathematical methods of quantum mechanics Mathematical aspects of Quantum Field Theory and String Theory Symplectic geometry, sub-Riemannian geometry Geometry of quantum fields and strings Seminar on Hodge theory ... [-]The aim of the Ph.D. Course in Mathematical Analysis, Modelling, and Applications is to educate graduate students in the fields of mathematical analysis and mathematical ... [+]

The aim of the Ph.D. Course in Mathematical Analysis, Modelling, and Applications is to educate graduate students in the fields of mathematical analysis and mathematical modeling, and in the applications of mathematical and numerical analysis to science and technology. The goal is to enable PhDs to work as high-level researchers in these fields in universities, research institutes, and private companies.

Research TopicsThe activity in Mathematical Analysis is mainly focused on ordinary and partial differential equations, on dynamical systems, on the calculus of variations, and on control theory. Connections of these topics with differential geometry and reduced order modeling are also developed.... [-]

The PhD curriculum in Mathematics of Natural, Social and Life Sciences at Gran Sasso Science Institute will lead the students to deal not only with the more traditional a ... [+]

The PhD curriculum in Mathematics of Natural, Social and Life Sciences at Gran Sasso Science Institute will lead the students to deal not only with the more traditional aspects of this discipline, such as Pure Mathematics, Partial Differential Equations and Mathematical Physics, but also with entirely new problems, requiring the development of the most appropriate tools to deal with the complexity, such as stochastic analysis and computational mathematics.

The curriculum consists of 4 years of study and research. During the first year, after initial training classes, students will be offered three main courses and a wide number of short courses, covering a large spectrum of topics. By the beginning of the second year students select a research project under the supervision of one (or more) of the mathematicians affiliated to GSSI.... [-]

The Ph.D. in “Computational Mathematics and Decision Sciences” aims at offering graduate students solid skills in Computational Mathematics, Computational Physics, Scient ... [+]

Models, mathematics, statistics, data, and algorithms are the foundations of our digital world. Computational methods and mathematical analysis are increasingly used for simulation, prediction, data evaluation, analysis, risk assessment, development, and optimization, in virtually every field of Science.

The Ph.D. in “Computational Mathematics and Decision Sciences” aims at offering graduate students solid skills in Computational Mathematics, Computational Physics, Scientific Computing, Statistics, Decision Sciences, Optimization, Machine Learning, as well as an interdisciplinary view of Applied Mathematics, Physics and decision processes under uncertainty. The program gives a solid theoretical and computational grounding for high-level research in universities, international research institutions, and industry.... [-]