∙ 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

## Mathematical Physics Seminar

Organizers

Matteo Gallone, Davide Guzzetti, Tamara Grava, Igor Krasovsky, Marcello Porta

Venue

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

2023-2024 Mathematical Physics Seminar

Date | Speaker | Title |
---|---|---|

22 Nov 2023 | Pierre Karim Emile Lazag (SISSA) | Hyperuniform determinantal point processes |

## 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.

**Topics:**

- Universality and Critical phenomena
- Gaussian integration, Feynman graphs and Linked Cluster Theorem
- Grassmann variables and Grassmann Gaussian integration
- Perturbation theory for Fermions using Grassmann variables
- 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 global geometry of compact Kähler manifols.

**Part I** – Basic notions. Hermitian and Kähler manifolds, harmonic theory, Kodaira Vanishing and Embedding, 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.