Ponentes
Mirjam Cvetic (UPenn): Generalized Global Symmetries and Nested Symmetry Theories
Generalized Global Symmetries of D-dimensional Quantum Field Theories (QFTs) can be interpreted in terms of (D+1)-dimensional bulk Symmetry Theory (SymTh), which often turns out to be a gapped Symmetry Topological Field Theory (SymTFT). In this setting interacting degrees of freedom arise as edge modes of a higher-dimensional bulk system. We further show that the combined (D + 1)-dimensional bulk and D-dimensional edge mode theory can serve as the edge modes of a (D+2)-dimensional bulk theory, which leads to a nested structure of SymThs. We show how this structure naturally arises in a number of string-based constructions of QFTs with both discrete and continuous symmetries.
Tudor Dimofte (U Edinburgh): Tannakian QFT: from sparks to quantum groups
In a topological quantum field theory (TQFT), extended operators are expected to organize themselves into categories (and higher categories) with various additional algebraic structures. However, from a physical perspective, these categories are often difficult to compute or identify directly. I'd like to present one systematic approach to analyzing line-like extended operators in 3d TQFT, as representations of Hopf algebras and generalized quantum groups -- by exploiting boundary conditions in the TQFT's to explicitly compute/identify the quantum groups themselves in physics. I'll discuss some applications, from rederiving old results in Chern-Simons theory to new results in supersymmetric gauge theories. Mathematically, our methods are based on implementing Tannaka duality in TQFT. (Based on work with Wenjun Niu, to appear this week.)
Jacques Distler (UT Austin): N=2 SCFTs of Class-S and Families of Hitchin Systems
I will pick up where Ron Donagi left off, and discuss the behaviour as the base curve C degenerates to a nodal curve (explaining the meaning of the twisting at the boundary of the moduli space). I will then turn to the new features that arise in Type-D (and beyond). Even locally (on the punctured disk), the situation is surprisingly more intricate than it was in Type-A.
Ron Donagi (UPenn): On theories of class S and the geometry of meromorphic Higgs bundles
We explore both local and global aspects of the geometry of meromorphic Higgs moduli space and its Hitchin map. (Work with A.Balasubramanian, J.Distler, N.Donagi, A.Herrero and C.Perez.)
Olivia Dumitrescu (U North Carolina Chapel Hill): Lagrangian geometries of the Dolbeault and the de Rham moduli spaces
I will illustrate a comparison between two diffeomorphic moduli spaces in rank 2, the Hitchin and the de Rham moduli spaces, in terms of lagrangians filling up the entire space. This talk is based on work in progress with Motohico Mulase.
Sergei Gukov (Caltech): TBA
Sungkyung Kang (U Oxford): Using equivariant Seiberg-Witten theory to detect exotic diffeomorphisms
Given any smooth 4-manifold bounding a Seifert manifold, the Seifert action on its boundary can be used to define their boundary Dehn twists. If the given 4-manifold is simply-connected, this Dehn twist is always topologically isotopic to the identity, but usually not smoothly isotopic, making it a very nice potential example of exotic diffeomorphisms. In this talk, we will show how one can apply Seiberg-Witten theory and finite cyclic group symmetry to show that for any Brieskorn homology sphere bounding a positive-definite 4-manifold, their boundary Dehn twists are always infinite-order exotic. We will also discuss how this strategy can also be used to prove the existence of an exotic diffeomorphism which stays exotic after two stabilizations. This is a joint work with JungHwan Park and Masaki Taniguchi.
Craig Lawrie (DESY): Higgs Branches of Eight-supercharge SCFTs and Symplectic Singularities
An eight-supercharge supersymmetric quantum field theory has a Higgs branch which is both a hyperkahler space and a symplectic singularity. A symplectic singularity admits a natural foliation by symplectic leaves, and this induces a partial ordering on the leaves given by inclusion. The physical interpretation of this partial ordering is that it encompasses all the patterns of partial Higgsing: each leaf is associated with an SCFT and the transverse slice between two leaves captures the parameters that need to be tuned to perform a Higgs branch renormalization group flow between the two theories. I will discuss this structure of the Higgs branch for a variety of 6d (1,0), 4d class S, and 3d field theories, using techniques from geometry, Hitchin systems, and SQFT.
Marta Mazzocco (UP Cataluña): Segre surfaces for the Painlevé equations
Motohico Mulase (UC Davis): Information behind a singular connection
On the moduli space of connections, some of the points have hidden geometric information. This talk is aimed at exploring a few hints about how we deal with these geometries.
Ana Péon-Nieto (U Santiago de Compostela): BAA branes from very stable subregular Hodge bundles
The seminal work of Hausel and Hitchin provides examples of dual BBB and BAA branes on the moduli space of Higgs bundles, the latter being given by upward flows from very stable regular nilpotent Higgs bundles. For very stable bundles, the BBB mirror of their downward flow is a priori computable, so it becomes customary to understand how many of these there are. I will show that the only very stable fixed points correspond to the zero nilpotent orbit (by Laumon) , the regular (by Hausel—Hitchin) and a special type of subregular nilpotent orbits that we call Hitchin subregular orbits. For the latter, I will propose a mirror BBB brane and provide evidence for this statement.
Laura Schaposnik (U Illinois Chicago): Quantization of branes and 3-manifolds
During the talk, we will introduce brane quantization following Witten and Gaiotto's recent work on Probing Quantization Via Branes. We will then consider its relation with the branes and 3-manifolds we introduced with Baraglia defined via actions of involutions on different moduli spaces, hoping to further our understanding of the relation between Higgs bundles and representations of higher-dimensional manifolds.
Eric Sharpe (Virginia Tech): An introduction to decomposition in quantum field theories
In this talk, I will give an introduction to `decomposition', a property of $d$-dimensional QFTs with global $(d-1)$-form symmetries. Decomposition is the observation that such quantum field theories are equivalent to disjoint unions of other quantum field theories, first observed in 2006 and studied in numerous examples and applications since. I will outline some basic examples in two and four dimensions, and as time permits, discuss various applications.
Szilárd Szabó (Alfréd Rényi Institute of Mathematics): Asymptotic geometry of non-abelian Hodge theory and Riemann--Hilbert correspondence in a rank three parabolic case
I report on joint work with M. Eper about Hitchin WKB-analysis on a real 4-dimensional moduli space of rank 3 Higgs bundles in genus 0. The approach uses previous results joint with T. Mochizuki.