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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 
• Symplectic geometry, sub-riemannian geometry

• Geometry of quantum fields and strings

Mathematical Physics Seminar


Matteo GalloneDavide GuzzettiTamara GravaIgor Krasovsky, Marcello Porta


SISSA Main Building, Wednesday 16:00-17:00, Room 136.

2023-2024 Mathematical Physics Seminar

Introduction to nonperturbative methods for fermionic models

This course presents techniques used to rigorously approach the analysis of statistical mechanical systems of interacting fermions on a lattice.


  1. Universality and Critical phenomena
  2. Gaussian integration, Feynman graphs and Linked Cluster Theorem
  3. Grassmann variables and Grassmann Gaussian integration
  4. Perturbation theory for Fermions using Grassmann variables
  5. Brydges-Battle-Federbush formula with applications.

Constructions of 4-manifolds

  • Description:

 We will review several constructions of smooth four-dimensional manifolds that have proven useful to unveil inequivalent smooth structures.  

Introduction to topological quantum field theory

The course provides a brief introduction to Topological Field Theories as infinite dimensional generalisation of classical localisation formulae in equivariant cohomology. It starts with an introduction to these latter subjects (Duistermaat-Heckman theorem, equivariant cohomology and Atiyah-Bott formula) and their extension on supermanifolds. It then continues supersymmetric quantum mechanics and its relation with Morse theory, gradient flow lines and Morse-Smale-Witten complex.

Topics in complex geometry

The aim of the course is to give an introduction to some topics of current interest in the globalgeometry of compact Kähler manifols.Part I – Basic notions. Hermitian and Kähler manifolds, harmonic theory, Kodaira Vanishing andEmbedding, Kempf-Ness Theorem, notions of canonical Kähler metrics.Some textbooks:

3-dimensional mirror symmetry and elliptic cohomology

This is an advanced course that will explore connections between recent developments in geom- etry, mathematical physics and homotopy theory. Its format will be that of a working seminar. Mirror symmetry has been at the center stage of geometry for the last thirty years. It is a sophisticated dictionary relating the symplectic geometry of a variety X and the algebraic ge- ometry of its mirror Y , and vice versa.

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