The (equivariant) Morse theory of the Yang-Mills functional was first studied by Atiyah and Bott, who found many beautiful connections with different areas of mathematics. One of the most well-known of these is the relationship between the (analytically defined) Morse strata and the (algebraically defined) Harder-Narasimhan strata. It is then natural to study spaces of Yang-Mills flow lines between critical points, however one is then confronted with the difficulty of solving the reverse Yang-Mills flow equations (which are modelled on a nonlinear heat equation). In this talk I will explain how to construct long-time solutions to the reverse Yang-Mills flow and how this leads to an algebraic classification of flow lines between critical points. There is also a geometric interpretation of flow lines in terms of secant varieties of the underlying Riemann surface, and if time permits I will explain how one can use these ideas to study \(C^*\) flow lines on the moduli space of rank 2 twisted Higgs pairs.

Día

Martes, 21 de xaneiro de 2025

Lugar

Aula 10
Facultade de Matemáticas