Date 
Speaker 
Title, Abstract 
October 25 
Michele Schiavina (ETH  Zürich)

BVBFV approach to General Relativity


The BVBFV formalism is a combination of the BV approach to quantisation of Lagrangian
field theories with local symmetries and the BFV approach to quantisation of constrained
Hamiltonian systems. It aims to assign compatible bulkboundary cohomological data to
a Lagrangian field theory on a manifold with boundary (and higher codimension strata),
in view of a perturbative quantisation scheme that is compatible with cutting and gluing.
General Relativity (GR), seen as a field theory, is a very important example to phrase
within this setting, and one in which interesting new insight and complications emerge
already at the classical level. In this talk I will present a summary of
investigations on GR within the BVBFV formalism, as well as other
diffeomorphisminvariant theories, which have given access to rich and
nontrivial information about the boundary structure of gravitational models.
However, I will argue that the featured examples present unexpected complications
for the program of quantisation with boundary (and higher strata). Indeed, I will show
how the BVBFV construction provides a filter to refine the notion of classical
equivalence of field theories, which distinguishes theories in terms of their
bulkboundary behaviour, suggesting that some realisations — among the class of
classically equivalent ones—may be more suitable for quantisation with boundary.
This allows us to differentiate between, e.g., metric and coframe gravity as well
as different string theory models and their 1d analogues. This is a summary of
joint works with G. Canepa and A.S. Cattaneo.

November 15 
Pavel Putrov (ICTP)

Nonsemisimple TQFTs and BPS qseries


In my talk I will describe a relation between the 3manifold invariant of CostantinoGeerPatureauMirand,
constructed from a nonsemisimple category of representations of a quantum group, and counting of BPS states
in a 6d (2,0) superconformal field theory complactified on a 3manifold with a topological twist. The talk
is based on a joint work with F. Costantino and S. Gukov.

November 22 
Ingmar Saberi (LMU)

Twisted elevendimensional supergravity and exceptional Lie algebras


In recent years, there has been a great deal of progress on ideas related to twisted supergravity,
building on the definition given by Costello and Li. Much of what is explicitly known about these theories
comes from the topological Bmodel, whose string field theory conjecturally produces the holomorphic twist
of type IIB supergravity. Progress on elevendimensional supergravity has been hindered, in part, by the lack
of such a worldsheet approach. I will discuss a rigorous computation of the twist of the free
elevendimensional supergravity multiplet, as well as an interacting BV theory with this field content
that passes a large number of consistency checks. Surprisingly, the resulting holomorphic theory on
flat space is closely related to the infinitedimensional exceptional simple Lie superalgebra \(E(5,10)\).
This is joint work with Surya Raghavendran and Brian Williams.

November 29 
Kevin Costello (Perimeter Institute)

Selfdual YangMills and anomaly cancellation on twistor space


YangMills theory in the first order formulation is a deformation of selfdual Yang Mills theory.
The latter theory is much simpler than full YangMills theory, and yet is surprisingly rich.
I will discuss the role of anomaly cancellation on twistor space plays in the study of this theory.

December 6 
Mykola Dedushenko (Simons Center  Stony Brook)

Quantum algebras and SUSY interfaces


I will talk about supersymmetric interfaces in gauge theories in the context of the Bethe/gauge
correspondence. These interfaces, viewed as operators on the Hilbert space, give linear maps between
spaces of SUSY vacua, understood mathematically as generalized cohomology theories of the Higgs branch.
A natural class of interfaces are SUSY Janus interfaces for masses, with the corresponding cohomological
maps being either the stable envelopes or the chamber Rmatrices (both due to MaulikOkounkov and
AganagicOkounkov). Thus, such interfaces (and their collisions) can be used to define actions of the
spectrum generating algebras (such as Yangians) on the “gauge” side of the Bethe/gauge correspondence, i.e.,
in QFT. Further applications and possible generalizations will be mentioned as well. Based on the recent
and upcoming works with N.Nekrasov.

December 13 
Justin Hilburn (Perimeter)

2Categorical 3d Mirror Symmetry


A 3d N=4 gauge theory T[G,X] is associated to a hyperKahler manifold X with a hyperHamiltonian
action of a compact Lie group G. Such a theory admits two topological twists. The Atwist is the
reduction of the DonaldsonWitten twist from 4d N=2 and the Btwist is also known as the RozanskyWitten
twist. There is a duality known as 3d mirror symmetry that exchanges the A twist of a 3d N=4 theory
with the Btwist of its mirror. This is closely related to 2d mirror symmetry and 4d electricmagnetic
duality which give rise to the celebrated "mirror symmetry" and geometric Langlands programs in
mathematics. It is expected that a 3d topological field theory is determined by its 2category of
boundary conditions. The 2category assigned to Btwisted 3d N=4 gauge theories has been described
in physics work of Kapustin, Rozansky, Saulina and mathematical work of Arinkin but the 2category
assigned to an Atwisted 3d N=4 theory has only been described in a few cases by Kapustin, Vyas,
Setter and in the pure gauge theory case by Teleman. In this talk I will describe work with Ben
Gammage and Aaron MazelGee on proving one formulation of 2categorical mirror symmetry for abelian
gauge theories.

December 20 
Yongbin Ruan (Zhejiang University)

Geometric Langlands and Coadjoint Orbits


Geometric Langlands concerns the mirror symmetry between Hitchin moduli space for
group G via the Hitchin moduli space of its Langlands dual. So far, majority of works are about the
moduli space without marked point/parabolic structure. It is generally understood that the insertion at
marked point is a (co)adjoint orbit of the Lie algebra. In order to have any chance for the mirror symmetry
of parabolic Hitchin moduli space, we must have a mirror symmetry among the insertions, i.e, coadjoint orbits.
This is a striking predication since coadjoint orbits are such classical objects in geometric presentation theory.
During the talk, we will explain a conjecture for mirror symmetry of coadjoint orbits and some partial results.
The conjecture is partially motivated by the seminal works of GukovWitten in physics. This is a
joint work with Yaoxiong Wen.

January 10 
Eric Sharpe (Virginia Tech)

An introduction to decomposition


In this talk I will review work on `decomposition,' a property of 2d theories
with 1form symmetries and, more generally, ddim'l theories with (d1)form
symmetries. Decomposition is the observation that
such quantum field theories are equivalent to ('decompose into’)
disjoint unions of other QFTs, known in this context as "universes.”
Examples include twodimensional gauge theories and
orbifolds with matter invariant under a subgroup of the gauge group.
Decomposition explains and relates several
physical properties of these theories  for example,
restrictions on allowed instantons arise as a "multiverse
interference effect" between contributions from constituent universes.
First worked out in 2006 as part of efforts to understand string propagation
on stacks, decomposition has been the driver of a number of developments since.
In the first half of this talk, I will review decomposition; in the
second half, I will focus on the recent application to anomaly resolution of
WangWenWitten in twodimensional orbifolds.

January 17 
Daniel Roggenkamp (Mannheim Universität)

Defects and Affine RozanskyWitten models


In this talk I will explain in the example of RozanskyWitten models with affine target spaces,
how, by means of the cobordism hypothesis, one can reconstruct an (extended) TQFT from its identity
defect. For illustration I will shoot a sparrow with a cannon and use defects to rederive the
state spaces of affine RW models for arbitrary surfaces.

January 24 
Surya Raghavendran (Perimeter)

Twisted Sduality


We identify a hidden \(SL_2(\mathbb C)\) symmetry of KodairaSpencer theory on CalabiYau 3folds.
Assuming some conjectures of CostelloLi, which posit descriptions of type II superstrings
in certain backgrounds as certain topological strings, we argue that this SL_2 C symmetry
comes from Sduality of type IIB. Time permitting, we'll discuss some applications of our
constructions to the Geometric Langlands program for GL_n. This talk is based on joint
work with Philsang Yoo.

January 31 
Tudor Dimofte (UC  Davis)

A QFT for nonsemisimple TQFT


Topological twists of 3d N=4 gauge theories naturally give
rise to nonsemisimple 3d TQFT's. In mathematics, prototypical
examples of the latter were constructed in the 90's (by Lyubashenko
and others) from representation categories of small quantum groups at
roots of unity; they were recently generalized in work of Costantino
GeerPatureau Mirand and collaborators. I will introduce a family of
physical 3d quantum field theories that (conjecturally) reproduce
these classic nonsemisimple TQFT's. The physical theories combine
ChernSimonslike and 3d N=4like sectors. They are also related to
FeiginTipunin vertex algebras, much the same way that Chern
Simons theory is related to WZW vertex algebras.
(Based on work with T. Creutzig, N. Garner, and N. Geer.)

February 7 
Jakob Palmkvist (Örebro University)

Non Linear Realization of Lie Superalgebras


The talk is based on 2012.10954. For any decomposition of a Lie superalgebra G into a direct sum G=H+E
of a subalgebra H and a subspace E, without any further resctrictions on H and E, we construct a nonlinear
realisation of G on E. The result generalises a theorem by Kantor from Lie algebras to Lie superalgebras.
When G is a differential graded Lie algebra, we show that it gives a construction of an associated
Linfinityalgebra.
