Date 
Speaker 
Title, Abstract 
September 25 
Du Pei (QGM Aarhus and Caltech) 
Can one hear the shape of a drum? 

Much like harmonics of musical instruments, spectra of quantum
systems contain wealth of interesting information. In this talk, I will
introduce new invariants of three and fourmanifolds using BPS spectra of
quantum field theories. While most of them are completely novel, some of
the new invariants categorify wellknown old invariants such as the WRT
invariant of 3manifolds and the Donaldson invariant of 4manifolds. This
talk is based on arXiv:1701.06567 and ongoing work with Sergei Gukov, Pavel
Putrov and Cumrun Vafa. 
October 16 
Laura Schaposnik (UIC) 
On Cayley and Langlands type correspondences for Higgs bundles. 

The Hitchin fibration is a natural tool through which one can understand
the moduli space of Higgs bundles and its interesting subspaces (branes). After reviewing
the type of questions and methods considered in the area, we shall dedicate this talk to the
study of certain branes which lie completely inside the singular fibres of the Hitchin fibrations.
Through Cayley and Langlands type correspondences, we shall provide a geometric description of these
objects, and consider the implications of our methods in the context of representation theory,
Langlands duality, and within a more generic study of symmetries on moduli spaces. 
November 6 
Natalie Paquette (Caltech) 
Dual boundary conditions in 3d N=2 QFTs 

We will study halfBPS boundary conditions in 3d N=2 field theories that
preserve 2d (0,2) supersymmetry on the boundary. We will construct
simple boundary conditions and study their local operator content using
a quantity called the halfindex. Using the halfindex as a guide, we
study the actions of a variety of 3d dualities on the boundary
conditions, including levelrank duality, mirror symmetry, and
Seiberglike duality. Identifying the dual pairs of boundary conditions,
in turn, helps lead to the construction of duality interfaces. This talk
is based on work in progress with T. Dimofte and D. Gaiotto.

November 7
Tuesday, 2pm, 02/104 
Arnav Tripathy (Harvard) 
Special cycles and BPS jumping loci 

I'll sketch an attempt to bring the theory of special cycles, a deep part of
number theory, into the domain of supersymmetric string compactifications. I'll describe a
construction based on jumping loci for BPS state counts  a separate phenomenon from the
betterknown wallcrossing!  and explain in what cases these jumping loci generalize some
parts of the theory of special cycles. Finally, I'll conclude with a host of physical and
mathematical conjectures raised by this line of investigation. 
November 20 
Minhyong Kim (Oxford) 
Gauge theory in arithmetic geometry I 

Numbertheorists have been implicitly using gauge theory for perhaps 350 years,
and explicitly for about 50 years. However, they did not use the terminology at all. I will
review some of this story and explain why it's a good idea do to so now. In particular, we will
describe some of the ideas of Diophantine gauge theory and arithmetic ChernSimons theory. 
November 21
Tuesday, 2pm, 02/104 
Minhyong Kim (Oxford) 
Gauge theory in arithmetic geometry II 

This is a continuation of the previous lecture 
December 4 
Lukas Hahn (Heidelberg) 
Super Riemann surfaces and their moduli 

Abstract forthcoming 
January 15 
Helge Ruddat (Mainz) 
Tropical construction of
Lagrangian submanifolds 

Homological mirror symmetry suggests that complex submanifolds of a
CalabiYau manifold match Lagrangian submanifolds of the mirror dual
CalabiYau. In practice, a maximal degeneration needs to be chosen and
then the submanifolds are identified by a duality of their degeneration
data which is tropical geometry. Cheuk Yu Mak and I carry out this
construction for lines on the quintic threefold which become spherical
Lagrangians in the quintic mirror. Our construction applies more
generally for CalabiYau threefolds in the Batyrev construction and
probably even more generally at some point in the future. Quite
surprisingly, many exotic Lagrangian threefolds can be constructed this
way, many for the first time in a compact symplectic 6manifold. 
February 19 
Guglielmo Lockhart (Amsterdam) 
Universal features of 6d selfdual string CFTs 

BPS strings are the fundamental objects on the tensor branch of 6d \((1,0)\) SCFTs. They can
be thought of as the instantons of the 6d gauge group, and are the building blocks for computing the
‘instanton piece’ of the \(\mathbb R^4\times T^2\) partition function of the parent 6d SCFT. The goal of this talk is to
rephrase their properties from the point of view of a worldsheet \(\mathcal N=(0,4)\) NLSM. This reveals that, despite
their superficial differences, selfdual strings of arbitrary 6d SCFTs share many universal features.
Along the way, this leads to a better understanding of the flavor symmetry of the parent 6d SCFTs.
Moreover, the constraints from modularity and these universal features are strong enough that one
can fix the elliptic genus of one selfdual string for a wide variety of SCFTs. 
February 26 
Jan Swoboda (München) 
The Higgs bundle moduli space and its asymptotic geometry 

The Theorem of Narasimhan and Seshadri states a correspondence between the moduli space
of stable holomorphic vector bundles over a Riemann surface \(X\) and that of irreducible unitary connections
of constant central curvature. This is one instance of a much more general correspondence due to Kobayashi
and Hitchin. Higgs bundles come into play when the compact Lie group \(\operatorname{SU}(r)\) is replaced by
\(\operatorname{SL}(r,\mathbb C)\). A suitable generalization of the constant central curvature connections in the
former case is found in the solutions to Hitchin's selfduality equations. Due to the noncompactness of
the Higgs bundle moduli space, a set of new questions revolving around its ``geometry at infinity'' arises.
In this talk I will focus on the asymptotics of the natural \(L^2\)metric \(G_{L^2}\) on the moduli space
\(\mathcal M\) of rank\(2\) Higgs bundles. I will show that on the regular part of the Hitchin fibration
\((A,\Phi)\mapsto\det\Phi\) this metric is wellapproximated by the semiflat metric \(G_{\operatorname{sf}}\)
coming from the completely integrable system on \(\mathcal M\). This also reveals the asymptotically
conic structure of \(G_{L^2}\), with (generic) fibres of the above fibration being asymptotically flat
tori. This result confirms some aspects of a more general conjectural picture made by Gaiotto, Moore
and Neitzke. Its proof is based on a detailed understanding of the ends structure of \(\mathcal M\).
The analytic methods used here in addition yield a complete asymptotic expansion of the difference
\(G_{L^2}G_{\operatorname{sf}}\) between the two metrics, with leading order term having polynomial
decay and a rather explicit description.
The results presented here are from recent joint work with Rafe Mazzeo, Hartmut Weiß and Frederik Witt.
