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Geometry and Mathematical Physics

∙ Integrable systems in relation with differential, algebraic and symplectic geometry, as well as with the theory of random matrices, special functions and nonlinear waves, Frobenius manifolds • Deformation theory, moduli spaces of sheaves and of curves, in relation with 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

Algebraic Geometry

Research topics

  • Construction of virtual classes and their use to define enumerative invariants; properties of the invariants and methods for their computations. Extension to orbifolds/smooth Deligne-Mumford algebraic stacks of constructions for manifolds, in particular Gromov-Witten invariants and Chen-Ruan cohomology.
  • Moduli spaces, such as moduli of (decorated) sheaves (including principal bundles, Higgs bundles, coherent systems, instantons), stable maps, varieties and Hilbert and Quot schemes. Deformation theory and additional structures such as algebraic stacks and dg-schemes. Hitchin-Kobayashi correspondence.
  • Applications to and relations with topological field theories and string theory.
  • Equivariant cohomology and localization formulas.

Integrable Systems, Frobenius Manifolds and Nonlinear Waves

Research Topics

  • Frobenius manifolds and quantum cohomologies.
  • Isomonodromy deformations with applications to the geometry of Frobenius manifolds and Painleve' type equations.
  • Moduli spaces in the theory of integrable systems.
  • Theory of nonlinear waves, oscillatory behavior, critical phenomena Painleve' equations and Riemann-Hilbert problems.
  • Theta-functions of Riemann surfaces, Painleve' transcendents and other special functions in integrable systems and nonlinear waves.
  • Integrable structures in random matrix theory and other random objects.

Seminars

Current Master Students

Future Conferences

Workshops and Conferences

COFIN and PRIN

  • Italian MIUR Research Project: Geometric and analytic theory of Hamiltonian systems in finite and infinite dimensions, 2013-2015, 2010-2011, 2007-2008, 2005-2006. P.I. B. Dubrovin, co-P.I. G. Falqui, T. Grava, D. Guzzetti.

European Networks

Geometry and Mathematical Physics

Purpose of the PhD Course

The PhD 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 wide spectrum of topics in modern algebraic and differential geometry and their applications.

Courses

Click here for the spring schedule of the courses.

 

Research Topics

  • Integrable systems in relation with 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 for moduli spaces of sheaves and of curves, in relation with 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, stochastic geometry, real algebraic geometry
  • Geometry of quantum fields and strings
  • Complex differential geometry
  • Generalized complex geometry

Lecture series

Seminars

iGAP

Geometers and Physicists collaborate within the iGAP project.

 

Admission to PhD Program

The Mathematics area at SISSA offers a doctoral program focused on Geometry and Mathematical Physics (GMP) and targeted to excellent students.

The GMP graduate program is entirely taught in English, and covers various topics of modern mathematics: algebraic geometry; real and complex differential geometry; stochastic and real algebraic geometry; non-commutative geometry; integrable structures in mathematics and physics, random matrices; special functions; nonlinear waves; geometry of strings and quantum fields; mathematical methods of quantum physics.

Students at SISSA have the possibility of studying and doing research in an international and active environment, interacting closely with professors and postdocs.

The GMP graduate program is structured as follows: during the first year, the students will complete their preparation by attending graduate courses (here is the list of the current courses), and the remaining years are dedicated exclusively to research.

Benefits for our students include:

  • mentoring programs
  • funding for summer schools and conferences
  • funding for 4 years (12 months/year stipend)
  • no teaching load (some light teaching is possible, if desired)
  • on-site kindergarten and maternity leave contribution
  • contribution toward housing expenses
  • language courses
  • rich seminar activity

Trieste is an international city, with a low cost of living. Together with ICTP, the University of Trieste, iGAP, and the AREA Science Park, SISSA contributes to make Trieste the perfect city for graduate studies.

SISSA promotes international research and our PhD program also has co-tutelle supervisions with many European institutions.

Deadline for applications: 03 February 2022
Interviews: 14--18 February 2022 (remotely)

Courses start on October 1st 2022.

The application process starts here.
For any inquiries, please write to: phd@sissa.it or visit the dedicated webpage.

 

PhD Coordinator for Geometry and Mathematical Physics

Faculty

Former Faculty Members

Former Professors

Visiting Professors

External Collaborators

Temporary Scientific Staff

PhD Students

Fourth Year Students

Third Year Students

Second Year Students

First Year Students

 

Previous PhD Theses

Click here to see the previous PhD Theses.

 

Regulation

Click here to see the regulation of this Ph.D. course (in Italian).

Geometry and Mathematical Physics

Mathematical Physics and Geometry are among the most rapidly developing branches of Pure and Applied Mathematics. The core activity of the SISSA group focuses on topics which are attracting a wide interest from the international scientific community. 

Group picture

 

Research Topics

The research of this group is diverse and multidisciplinary. Professors, post-doctoral fellows and graduate students face problems in integrable systems, in relation with differential, symplectic and algebraic geometry, as well as special functions and nonlinear waves; noncommutative geometry, geometry of strings and quantum fields and mathematical methods of quantum physics; stochastic geometry and real algebraic geometry. The will to understand the intimate connection between Physics and Geometry has lead to a collaboration between different areas of research at SISSA, culminating in the iGAP project.

Faculty

Former Faculty Members

Former Professors

Visiting Professors

External Collaborators

Temporary Scientific Staff

Seminars

Click here to see the seminars of this research group.

 

Events and Workshops

Click here to see events and workshops  organized by this research group.

 

Publications

Click here to see the publications of this research group.

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