International School for Advanced Studies (SISSA)
PhD in Geometry and Mathematical PhysicsDEGREE TYPE
PhD
DURATION
4 years
LANGUAGES
English
PACE
Full time
APPLICATION DEADLINE
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EARLIEST START DATE
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STUDY FORMAT
On-Campus
Key Summary
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Introduction
Purpose of the Ph.D. Course
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 students of the Geometry and Mathematical Physics sector organize a series of seminars on topics of Hodge Theory.
The most recent placements after Ph.D. at SISSA:
- Mathematical Sciences Research Institute Berkeley - USA,
- Harvard University, Cambridge - USA,
- Mathematical Institute, University of Oxford - UK,
- DAMTP, University of Cambridge - UK,
- Max Planck Institute, Bonn - Germany,
- École Polytechnique, Palaiseau - France
Curriculum
General Rules
The Ph.D. programme consists of three/four years of study and research.
The main selection procedure consists in an entrance examination. This is divided into two parts: in the written part applicants are asked to solve problems from a list given by the entrance committee. The oral exam consists of a discussion on the written test, on the topics studied in the university curriculum, and possibly on the applicant's thesis for the university degree or on other scientific achievements. The applicant's scientific qualifications and references are also taken into account.
Non-EU citizens may be admitted on the sole basis of their previous scientific activity, publications, and references, in a pre-selection procedure. They have to pass a "Qualifying Examination" at the end of their first year.
A student may choose among different plans of study oriented to the different fields covered by their Ph.D. course. In the first month of the Ph.D. programme, the faculty approves the individual plans of study, taking into account the scientific interests of the students and the skills already acquired in the previous university studies.
In the first year, students attend both basic and more advanced courses. To be admitted to the second year they are required to pass the examinations of the courses included in their plan of study. Students are invited to attend, without examinations, also some courses in fields different from those of their plan of study.
At the end of the first year, students start a research project, under the supervision of a faculty member or of an external collaborator approved by the faculty, in one of the research fields of the Ph.D. programme.
During the second and third-year students work on their research projects, participate in the seminar activities of the Ph.D. programme, and attend some courses. Examinations have to be passed only by students who worked in their first year in a different Ph.D. programme.
Students obtain the Ph.D. degree after submitting their Ph.D. thesis and defending it in front of an examination committee, whose members include SISSA staff members and international experts in the field. SISSA Ph.D. in one of the courses of Mathematics Area is by law equivalent to the Italian degree of “Dottore di Ricerca in Matematica”.