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

Beginning on Sunday, May 28 and ending Friday June 2, 2023

All times in UBC Okanagan, Canada time, PDT (UTC-7).

Sunday, May 28
16:00 - 23:00 Check-in Begins at 16:00 and Is Open 24 Hours
Nechako Residence Building, UBCO
(Other (See Description))
Monday, May 29
08:00 - 08:45 Breakfast (Sunshine/ADM)
08:45 - 09:00 Introduction and Welcome by BIRS-UBCO Staff
Main Meeting Room (ARTS 103), UBCO
(Other (See Description))
09:00 - 10:00 Emily Cliff: Quasi-universal sheaves and generic modules
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
(Other (See Description))
10:00 - 10:30 Coffee Break
Break Room (ARTS 112), UBCO
(Other (See Description))
10:30 - 11:30 Adam Sikora: From quantum topology to character varieties
Main Meeting Room (ARTS 103), UBCO
(Other (See Description))
11:30 - 13:00 Lunch (Sunshine/ADM)
13:00 - 13:20 Group Photo
Group photo to be taken outside. We will meet at ARTS 103 at 1:00 pm PT before departing together.
(Other (See Description))
13:30 - 14:30 Giulio Collinucci: CY3s and nilpotent spectral data
Main Meeting Room (ARTS 103), UBCO
(Other (See Description))
15:00 - 15:30 Coffee Break
Break Room (ARTS 112), UBCO
(Other (See Description))
17:30 - 19:00 Dinner (Sunshine/ADM)
Tuesday, May 30
08:00 - 09:00 Breakfast (Sunshine/ADM)
09:00 - 10:00 Ruxandra Moraru: Hitchin pairs on higher-dimensional manifolds
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
(Other (See Description))
10:00 - 10:30 Coffee Break
Break Room (ARTS 112), UBCO
(Other (See Description))
10:30 - 11:30 Andrew Neitzke: Wall crossing and geometry of Higgs bundles
Main Meeting Room (ARTS 103), UBCO
(Other (See Description))
11:30 - 14:00 Lunch (Sunshine - Administration Building)
14:00 - 15:00 Christian Pauly: On very stable bundles
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
(Other (See Description))
15:00 - 15:30 Coffee Break
Break Room (ARTS 112), UBCO
(Other (See Description))
15:30 - 17:00 Open Problem Session
Break Room (ARTS 112), UBCO
(Other (See Description))
17:30 - 19:00 Dinner (Sunshine/ADM)
Wednesday, May 31
08:00 - 08:45 Breakfast (Sunshine/ADM)
09:00 - 10:00 Julius Grimminger: Singular hyper-Kähler varieties and their smooth strata
Main Meeting Room (ARTS 103), UBCO
(Other (See Description))
10:00 - 10:30 Coffee Break
Break Room (ARTS 112), UBCO
(Other (See Description))
10:30 - 11:30 Max Huebner: Punctures and symmetries in class S
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
(Other (See Description))
11:30 - 13:00 Lunch (Sunshine/ADM)
13:00 - 17:30 Free Afternoon (Kelowna)
17:30 - 19:00 Dinner (Sunshine/ADM)
Thursday, June 1
08:00 - 09:00 Breakfast (Sunshine/ADM)
09:00 - 10:00 Sebastian Schulz: Conformal Limits and the partial oper stratification
Main Meeting Room (ARTS 103), UBCO
(Other (See Description))
10:00 - 10:30 Coffee Break
Break Room (ARTS 112), UBCO
(Other (See Description))
10:30 - 11:30 Eric Boulter: Generalizations of Higgs bundles on elliptic surfaces of non-Kähler type
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
(Other (See Description))
11:30 - 14:00 Lunch (Sunshine - Administration Building)
14:00 - 15:00 Craig Lawrie: To construct a=c theories: non-Lagrangian quivers
Main Meeting Room (ARTS 103), UBCO
(Other (See Description))
15:00 - 15:30 Coffee Break
Break Room (ARTS 112), UBCO
(Other (See Description))
17:30 - 19:00 Dinner (Sunshine/ADM)
Friday, June 2
08:00 - 09:00 Breakfast - *Please Note That Residence Check-Out Must Be Complete by 11:00 (Sunshine - Administration Building)
09:00 - 10:00 Christopher Mahadeo: Twisted Higgs bundles and topological recursion
Main Meeting Room (ARTS 103), UBCO
(Other (See Description))
10:00 - 10:30 Coffee Break
Break Room (ARTS 112), UBCO
(Other (See Description))
10:30 - 11:30 Monica Kang: Finding isomorphic 4d SCFTs via geometrization
Main Meeting Room (ARTS 103), UBCO
(Other (See Description))
11:30 - 13:30 Lunch (Sunshine - Administration Building)