Schedule for: 23w5082 - The Geometry, Algebra, and Physics of Higgs Bundles

Nechako Residence Building, UBCO

Main Meeting Room (ARTS 103), UBCO

This is based on joint work-in-progress with Colin Ingalls and Charles Paquette. Given a finite-dimensional algebra, we can associate a quiver and choose a dimension vector. Work of Alistair King shows that, if the dimension vector is unimodular, there is a moduli space of stable representations with a universal sheaf. Work of Reineke--Schröer and Hoskins--Schaffhauser shows that this does not hold for all dimension vectors; in general, we obtain a only "quasi-universal sheaf". I will discuss this construction from several perspectives, and explain applications to the representation theory of finite-dimensional algebras. Main Meeting Room (ARTS 103), UBCO

Break Room (ARTS 112), UBCO

Main Meeting Room (ARTS 103), UBCO

Group photo to be taken outside. We will meet at ARTS 103 at 1:00 pm PT before departing together.

Main Meeting Room (ARTS 103), UBCO

Break Room (ARTS 112), UBCO

In this talk, we discuss generalizations of Higgs bundles on curves to higher-dimensional manifolds, consisting of pairs $(E,\phi)$ with $E$ a holomorphic vector bundle on a complex manifold $X$ and $\phi \in H^0(X,End(E) \otimes V)$, where $V$ is a fixed holomorphic vector bundle on $X$. For example, when $V = K_X$, stable pairs $(E,\phi)$ correspond to solutions of the Vafa-Witten equations, and when $V = T^*_X$ (resp. $T_X$), such pairs are called Higgs (resp. co-Higgs) bundles. I will given an overview of some of the known results about Hitchin pairs in higher dimensions and describe some open problems. Main Meeting Room (ARTS 103), UBCO

Break Room (ARTS 112), UBCO

Main Meeting Room (ARTS 103), UBCO

A very stable vector bundle over a curve is a vector bundle having no non-zero nilpotent Higgs fields. They were introduced by Drinfeld and studied by Laumon in connection with the nilpotent cone of the Hitchin system. According to Drinfeld non-very stable bundles, also called wobbly bundles, form a divisor in the moduli space of vector bundles. In this talk I will try to explain the motivations for studying the properties of wobbly divisors, with a special focus on the rank-2 (joint work with S. Pal) and rank-3 case (joint work with A. Peon-Nieto). Main Meeting Room (ARTS 103), UBCO

Break Room (ARTS 112), UBCO

Break Room (ARTS 112), UBCO

Main Meeting Room (ARTS 103), UBCO

Break Room (ARTS 112), UBCO

We discuss the generalized global symmetries of 4d N=2 class S theories. These are encoded in the Seiberg-Witten curve of the theory and its IIB geometric dual. Based on work with Lakshya Bhardwaj, Sakura Schäfer-Nameki and Simone Giacomelli. Main Meeting Room (ARTS 103), UBCO

Main Meeting Room (ARTS 103), UBCO

Break Room (ARTS 112), UBCO

We give an overview of the spectral theory for vector bundles on a family of non-Kähler elliptic surfaces, and use this theory to determine existence criteria for generalizations of Higgs bundles on these surfaces (including co-Higgs bundles and Vafa-Witten bundles). We state some applications to holomorphic Poisson structures on projective line bundles and to singularities in moduli spaces of vector bundles. (Joint with R. Moraru.) Main Meeting Room (ARTS 103), UBCO

Main Meeting Room (ARTS 103), UBCO

Break Room (ARTS 112), UBCO

Main Meeting Room (ARTS 103), UBCO

Break Room (ARTS 112), UBCO

Main Meeting Room (ARTS 103), UBCO