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. The second part of the course is devoted to supersymmetric sigma models, their topological twist to the A and B models and the relation of the latters with Gromov-Witten theory and Landau-Ginzburg models and Hodge variations respectively. In the last part of the course we discuss supersymmetric gauged linear sigma models, vortices and mirror symmetry, and we provide the construction of mirror pairs for toric varieties.

## Introduction to Topological Field Theories

Lecturer:

Course Type:

PhD Course

Academic Year:

2022-2023

Duration:

40 h

Description:

Research Group: