| Date |
Speaker |
Title, Abstract |
| October 25 |
Michele Schiavina (ETH - Zürich)
|
BV-BFV approach to General Relativity
|
| |
The BV-BFV 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 bulk-boundary 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 BV-BFV formalism, as well as other
diffeomorphism-invariant 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 BV-BFV construction provides a filter to refine the notion of classical
equivalence of field theories, which distinguishes theories in terms of their
bulk-boundary 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)
|
Non-semisimple TQFTs and BPS q-series
|
| |
In my talk I will describe a relation between the 3-manifold invariant of Costantino-Geer-Patureau-Mirand,
constructed from a non-semisimple category of representations of a quantum group, and counting of BPS states
in a 6d (2,0) superconformal field theory complactified on a 3-manifold with a topological twist. The talk
is based on a joint work with F. Costantino and S. Gukov.
|
| November 22 |
Ingmar Saberi (LMU)
|
Twisted eleven-dimensional 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 B-model, whose string field theory conjecturally produces the holomorphic twist
of type IIB supergravity. Progress on eleven-dimensional 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
eleven-dimensional 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 infinite-dimensional exceptional simple Lie superalgebra \(E(5,10)\).
This is joint work with Surya Raghavendran and Brian Williams.
|
| November 29 |
Kevin Costello (Perimeter Institute)
|
Self-dual Yang-Mills and anomaly cancellation on twistor space
|
| |
Yang-Mills theory in the first order formulation is a deformation of self-dual Yang- Mills theory.
The latter theory is much simpler than full Yang-Mills 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 R-matrices (both due to Maulik-Okounkov and
Aganagic-Okounkov). 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)
|
2-Categorical 3d Mirror Symmetry
|
| |
A 3d N=4 gauge theory T[G,X] is associated to a hyper-Kahler manifold X with a hyper-Hamiltonian
action of a compact Lie group G. Such a theory admits two topological twists. The A-twist is the
reduction of the Donaldson-Witten twist from 4d N=2 and the B-twist is also known as the Rozansky-Witten
twist. There is a duality known as 3d mirror symmetry that exchanges the A twist of a 3d N=4 theory
with the B-twist of its mirror. This is closely related to 2d mirror symmetry and 4d electric-magnetic
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 2-category of
boundary conditions. The 2-category assigned to B-twisted 3d N=4 gauge theories has been described
in physics work of Kapustin, Rozansky, Saulina and mathematical work of Arinkin but the 2-category
assigned to an A-twisted 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 Mazel-Gee on proving one formulation of 2-categorical 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 Gukov-Witten 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 1-form symmetries and, more generally, d-dim'l theories with (d-1)-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 two-dimensional 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
Wang-Wen-Witten in two-dimensional orbifolds.
|
| January 17 |
Daniel Roggenkamp (Mannheim Universität)
|
Defects and Affine Rozansky-Witten models
|
| |
In this talk I will explain in the example of Rozansky-Witten 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 S-duality
|
| |
We identify a hidden \(SL_2(\mathbb C)\) symmetry of Kodaira-Spencer theory on Calabi-Yau 3-folds.
Assuming some conjectures of Costello-Li, which posit descriptions of type II superstrings
in certain backgrounds as certain topological strings, we argue that this SL_2 C symmetry
comes from S-duality 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 non-semisimple TQFT
|
| |
Topological twists of 3d N=4 gauge theories naturally give
rise to non-semisimple 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-
Geer-Patureau Mirand and collaborators. I will introduce a family of
physical 3d quantum field theories that (conjecturally) reproduce
these classic non-semisimple TQFT's. The physical theories combine
Chern-Simons-like and 3d N=4-like sectors. They are also related to
Feigin-Tipunin 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
L-infinity-algebra.
|
| Date |
Speaker |
Title, Abstract |
| April 12 |
Eiichiro Komatsu (Max-Plank-Institute for Astrophysics - Münich)
|
Three tales of de Sitter
|
| |
Based on works (to appear) with Lorenzo Di Pietro (Trieste) and Victor Gorbenko (Stanford).
I will discuss several novel perspectives on quantum field theory in de Sitter spacetime and dS/CFT.
The topics to be discussed include
1. Description of the dual CFT that directly produces the late-time correlation functions
(rather than the wave functions).
2. New connection to theories in AdS.
3. Unitarity and analyticity of the late-time correlation functions.
|
| April 19 |
Francesco Benini (SISSA - Trieste)
|
Superconformal Index and Gravitational Path Integral
|
| |
AdS/CFT provides a consistent non-perturbative definition of quantum gravity in asymptotically AdS spacetimes.
Black holes should correspond to ensembles of states in the boundary field theory. By performing a careful analysis
of the superconformal index of 4d N=4 SU(N) Super-Yang-Mills theory, with the help of a Bethe Ansatz type formula,
we are able to exactly reproduce the Bekenstein-Hawking entropy of BPS black holes in AdS5 x S5. The large N limit
exhibits many competing contributions, that we are able to identify with complex saddles of the (putative)
gravitational path-integral. Along the way we propose a necessary condition for complex saddles to contribute,
based on the size of their non-perturbative corrections. Such a prescription exactly matches the field theory analysis.
|
| April 26 |
Mathew Bullimore (Durham University)
|
Towards a Mathematical Definition of the 3d Superconformal Index
|
| |
The aim of this talk is to give a mathematical definition of the superconformal index counting local operators in
gauge theories with 3d N = 2 supersymmetry. This can be computed exactly using supersymmetric localisation,
which leads to an explicit contour integral formula involving infinite q-Pochhammer symbols. I will explain how
this result can be interpreted as the Witten index of a supersymmetric quantum mechanics, or index of a twisted
Dirac operator on a certain infinite-dimensional space. To illustrate the essential points, I will
focus on a concrete example of supersymmetric Chern-Simons theory.
|
| May 3 |
Miguel Montero (Harvard University)
|
Cobordisms, Anomalies, and the Swampland
|
| |
The Swampland program aims at constraining the EFTs that can be consistently coupled to quantum gravity from general
principles. In particular cases, absence of global symmetries can lead to strong constraints at low
energies. In this talk I will explain how this works and illustrate this in the particular context of
supersymmetric theories in d>6. In particular, vanishing of certain cobordism classes requires existence
of singular defects, which we call "I-folds". I-fold compactifications can have anomalies, rendering the
theory inconsistent. In this way, we find additional constraints in the rank of the gauge group.
The resulting constraints establish Coulomb branch string universality: The only consistent supergravities
in 8d and 9d are precisely those that arise from string compactifications.
I will also briefly comment on applications of these techniques to other interesting setups.
|
| May 10 |
Lukas Woike (University of Copenhagen)
|
Higher structures from modular categories
|
| |
Modular categories form a class of categories relevant in the representation theory of Hopf algebras
and conformal field theory, where they can be obtained from vertex operator algebras. Thanks to a
result of Bartlett, Douglas, Schommer-Pries and Vicary, a semisimple modular category is equivalent
to a once-extended (anomalous) three-dimensional topological field theory. Handling non-semisimple
modular categories is more involved, especially if one wants to take their non-trivial homological
algebra into account. In my talk, I will explain how to give a meaning to the homological algebra
of a modular category from the point of view of low-dimensional topology. In particular, I will discuss
the construction of differential graded conformal blocks with homotopy coherent mapping class group
representations, but also higher multiplicative structures and the connection to modified traces.
As a motivating example, I will discuss these higher structures for Dijkgraaf-Witten theory,
a discrete version of Chern-Simons theory. This is joint work with Christoph Schweigert.
|
| May 17 |
Cyril Closset (University of Birmingham)
|
Rank-1 5d SCFTs: Mapping out the U-plane
|
| |
The simplest non-trivial 5d superconformal field theories are arguably the famous rank-one theories with En global symmetry,
first discovered by Seiberg, which are ultraviolet completions of 5d N=1 supersymmetric SU(2) gauge theories with n-1 flavors.
In a work to appear with Horia Magureanu, we revisit various aspects of their Coulomb branch physics upon compactification
on a circle, using the known En Seiberg-Witten curves. The total space of the En curve fibered over the U-plane (the Coulomb branch)
can be described as a rational elliptic surface. These surfaces were classified long ago by Persson and Miranda, and the 5d
perspective gives us an interesting physical way to look at that classic mathematical result. I will describe in some detail
the various `massless points' in the parameters space of the field theory, where the flavor symmetry enhances from the generic
U(1)n to a semi-simple Lie algebra, and/or where Argyres-Douglas theories live. I will also discuss the interesting cases when
the U-plane is a modular curve. Finally, I will briefly talk about the 5d BPS quivers that can be associated to special points
on the U-plane. Our results shed some interesting five-dimensional light on the study of topological strings on local Calabi-Yau
threefolds.
|
| June 14 |
John Huerta (University of Lisbon)
|
Bundle gerbes on Lie supergroups
|
| |
Bundle gerbes are analogues of line bundles important for conformal field theory, anomalies, and obstruction theory.
Among bundle gerbes, a central role is played by the basic bundle gerbe, an essentially unique gerbe on any compact,
simple and simply-connected Lie group. In this talk, we describe our work constructing the basic bundle gerbe for a large
family of simple Lie supergroups, and show how the basic gerbe on a Lie supergroup decomposes into a tensor product of
gerbes on the underlying Lie group and an auxiliary 2-form.
|
| June 21 |
Johanna Knapp (University of Melbourne)
|
Genus 1 fibered Calabi-Yau 3-folds with 5-sections - A GLSM perspective
|
| |
Elliptic and genus one fibered Calabi-Yau spaces play a prominent role in string theory and mathematics. In this talk we will
discuss examples and properties of a class of genus one fibered Calabi-Yau threefolds with 5-sections. These Calabi-Yaus cannot
be constructed by means of toric geometry. One way to obtain them is as vacuum manifolds of gauged linear sigma models (GLSMs)
with non-abelian gauge groups. This approach makes it possible to find connections between different genus one fibrations with
5-sections that fit into the framework of homological projective duality. Furthermore we briefly discuss applications in
topological string theory and M-/F-theory. This is joint work with Emanuel Scheidegger and Thorsten Schimannek.
|
| July 5 |
Jan Manschot (Trinity College - Dublin)
|
Topological correlators of N=2* Yang-Mills theory
|
| |
N=2* Yang-Mills theory is a mass deformation of N=4 Yang-Mills, which preserves N=2 supersymmetry.
I will consider the topological twist of this theory with gauge group SU(2) on a smooth, compact four-manifold X.
A consistent formulation requires coupling of the theory to a Spin-c structure, which is necessarily non-trivial
if X is non-spin. I will discuss the contribution from the Coulomb branch to correlation functions in terms of the
low energy effective field theory coupled to a Spin-c structure, and present how these are evaluated using mock modular
forms. Upon varying the mass, the correlators can be shown to reproduce correlators of Donaldson-Witten theory as well
as Vafa-Witten theory. Based on joint work with Greg Moore, arXiv:2104.06492.
|
| Date |
Speaker |
Title, Abstract |
| October 12 |
Ezra Getzler (Northwestern)
|
Gluing local gauge conditions in BV quantum field theory
|
| |
In supersymmetric sigma models, there is frequently no global choice of
Lagrangian submanifold for BV quantization. I will take the superparticle, a
toy version of the Green-Schwarz superstring, as my example, and show how
to extend the light-cone gauge to the physically relevant part of phase space.
This involves extending a formula of Mikhalkov and A. Schwarz that generalizes
the prescription of Batalin and Vilkovisky for the construction of the functional
integral. This is joint work with S. Pohorence
|
| October 19 |
Christopher Beem (Oxford)
|
Hall-Littlewood Chiral Rings and Derived Higgs Branches
|
| |
I will discuss a relatively novel algebraic structure arising in four-dimensional N=2 superconformal
field theories: the Hall-Littlewood Chiral Ring. The HLCR is in a refinement of the more familiar
Higgs branch chiral ring which encodes the Higgs branch of the moduli space of vacua as an algebraic
variety. The HLCR in gauge theories is constructed as the cohomology of a kind of BRST complex,
which allows it to be identified with the ring of functions on the derived Higgs branch (in the
sense of derived algebraic geometry). I will describe the solution of the HLCR cohomology problem
for a large class of Lagrangian theories (the class S theories of type A1), which illustrate a
number of key features.
|
| October 26 |
Theo Johnson-Freyd (Dalhousie)
|
3+1d topological orders with (only) an emergent fermion
|
| |
There are exactly two bosonic 3+1d topological orders whose only nontrivial quasiparticle is an emergent fermion
(and exactly one whose only nontrivial quasiparticle is an emergent boson). I will explain the meaning of this
sentence: I will explain what a "3+1d topological order" is, and how I know that these are the complete list.
Time permitting, I will you some details about these specific topological orders, and say what this classification
has to do with "minimal modular extensions".
|
| November 2 |
Matthias Traube (LMU - München)
|
Cardy Algebras, Sewing-Constraints and String-Nets
|
| |
In this talk I will bring together three different concepts surrounding categorial description for RCFTs. Firstly,
Cardy algebras were introduced by Kong in order to describe the genus zero and one part of full open-closed RCFTs.
Secondly, string-nets were shown by Kirillov to compute the state of the Reshetikhin-Turaev three dimensional
topological field theory. I will bring the two ingredients together, in order to show the third one. That is, I
will show how Cardy algebra colored string-nets solve the sewing constraints, thereby giving rise to consistent
correlators in full open-close RCFTs and vice versa. The talk is based on the preprint: arXiv:2009.11895.
|
| November 9 |
Ilka Brunner (LMU - München)
|
Flow Defects and Phases of gauged linear sigma models
|
| |
I will discuss a special class of defects in two dimensional supersymmetric theories.
These "flow defects" connect UV and IR theories. They can in particular be used in the context of
gauged linear sigma models, where they connect different phases. Here, they can be regarded as
functors between brane categories and provide a new point of view on the "grade restriction rule"
initially proposed by Herbst, Hori and Page.
|
| November 16 |
Owen Gwilliam (Amherst)
|
Centers of higher enveloping algebras and bulk-boundary systems
|
| |
The universal enveloping algebra of a Lie algebra plays a key role in representation theory
(for obvious reasons) and in physics, particularly in encoding symmetries of quantum systems.
But it is just one in a family of higher enveloping algebras: each dg Lie algebra g has
an enveloping E_n algebra U_n(g). (Here E_n refers to "n-dimensional algebras" in the sense of
the little n-disks operad.) This construction admits a nice presentation via factorization algebras,
by work of Knudsen, and we will discuss how it relates to symmetries of quantum field theories.
We will discuss a model for the *center* of U_n(g) and how this framework encodes the observables
of a bulk-boundary system where the bulk is topological BF theory for Lie algebra g and the boundary
encodes "topological currents." (This is joint work with Greg Ginot, Brian Williams,
and Mahmoud Zeinalian.)
|
| November 30 |
Jörg Teschner (Universität Hamburg / Desy)
|
Proposal for a Geometric Characterisation of Topological String Partition Functions
|
| |
We propose a geometric characterisation of the topological string partition functions associated to
the local Calabi-Yau (CY) manifolds used in the geometric engineering of d = 4, N = 2 supersymmetric
field theories of class S. A quantisation of these CY manifolds defines differential operators called
quantum curves. The partition functions are extracted from the isomonodromic tau-functions associated
to the quantum curves by expansions of generalised theta series type. It turns out that the partition
functions are in one-to-one correspondence with preferred coordinates on the moduli spaces of quantum
curves defined using the Exact WKB method. The coordinates defined in this way jump across certain
loci in the moduli space. The changes of normalisation of the tau-functions associated to these
jumps define a natural line bundle.
|
| December 7 |
Susanne Reffert (Universität Bern)
|
The Large Charge Expansion
|
| |
It has become clear in recent years that working in sectors of large global charge of strongly coupled
and otherwise inaccessible CFTs leads to important simplifications. It is indeed possible to formulate
an effective action in which the large charge appears as a control parameter. In this talk, I will explain
the basic notions of the large-charge expansion using the simple example of the O(2) model and then
generalize to the non-Abelian case which has a richer structure and exhibits new effects.
|
| December 14 |
Dmitri Bykov (LMU - Munchen)
|
Sigma models as Gross-Neveu models
|
| |
I will show that there is a wide class of integrable sigma models, which includes CP^{n-1}, Grassmannian,
flag manifold models, that are equivalent to bosonic (and mixed bosonic/fermionic) chiral Gross-Neveu models.
The established equivalence allows to effortlessly construct trigonometric/elliptic deformations,
provides a new look on the supersymmetric theory and on the cancellation of anomalies in the integrability
charges. Using this formalism, we develop criteria for constructing quantum integrable models related to
quiver varieties. Based on arXiv:2006.14124 and arXiv:2009.04608.
|
| January 11 |
Kasia Rejzner (University of York)
|
BV-BFV formalism in perturbative AQFT
|
| |
BV-BFV formalism is a general framework for quantising gauge
theories on manifolds with boundary. In this talk I will present some
ideas on how to incorporate this framework into perturbative algebraic
quantum field theory (pAQFT), which is a mathematically rigorous
approach to QFT. After discussing general ideas, I will focus on their
application to the study of asymptotic structure of quantum
electrodynamics.
|
| January 25 |
Simeon Hellerman (IPMU)
|
The Large Quantum Number Expansion: Some Recent Developments
|
| |
This is a continuation, with a view toward applications, of the talk by Susanne Reffert given on 7/12/2020
|
| February 2 |
Andrea Brini (University of Sheffield)
|
Quantum Geometry and Physics of Looijenga Pairs
|
| |
A Looijenga pair is a pair (X,D) with X a smooth complex projective surface and D a singular
anticanonical divisor in X. I will describe a series of correspondences relating five
different classes of string-theory motivated invariants specified by the geometry of (X,D):
- the log Gromov--Witten theory of (X,D),
- the Gromov--Witten theory of X twisted by the sum of the dual line bundles to the irreducible components of D,
- the open Gromov--Witten theory of special Lagrangians in a toric Calabi--Yau 3-fold determined by (X,D)
- the Donaldson--Thomas theory of a symmetric quiver specified by (X,D), and
- a class of BPS invariants considered in different contexts by Klemm--Pandharipande, Ionel--Parker,
and Labastida--Marino--Ooguri--Vafa.
I will also show how the problem of computing all these invariants is closed-form solvable.
This is joint work with P. Bousseau (Saclay) and M. van Garrel (Warwick).
|
| Date |
Speaker |
Title, Abstract |
| February 17 |
Navid Nabijou (Glasgow) |
Tangent curves, degenerations, and blowups |
| |
It is well-known that every smooth plane cubic E supports precisely 9 flex lines.
By analogy, we may ask: "How many degree d curves intersect E in a single point?" The problem
of calculating such numbers of tangent curves has fascinated enumerative geometers for decades.
Despite being an extremely classical and concrete problem, it was not until the advent of Gromov-Witten
invariants in the 1990s that a general method was discovered. The resulting theory is incredibly rich,
and the curve counts satisfy a suite of remarkable properties, some proven and some still conjectural.
In this talk, I will discuss two distinct projects which take inspiration from this geometry. In
the first, joint with Lawrence Barrott, we study the behaviour of tangent curves as the cubic E
degenerates to a cycle of lines. Using the machinery of logarithmic Gromov-Witten theory, we
obtain detailed information concerning how the tangent curves degenerate along with E. The resulting
theorems are purely classical, with no reference to Gromov-Witten theory, but they do not appear
to admit a classical proof. In a separate project, joint with Dhruv Ranganathan, we perform iterated
blowups of moduli spaces to prove the so-called local-logarithmic conjecture for hyperplane sections;
this gives access to a large number of previously unknown enumerative theories.
No prior knowledge of Gromov-Witten theory will be assumed. |
| Mai 5 |
Ivo Sachs (Munich) |
From BV to string theory and back |
| |
abstract forthcoming... |
| Mai 18 |
Nils Carqueville (Vienna) |
An introduction to functorial TQFT with defects |
| |
abstract forthcoming... |
| Mai 25 |
Christoph Chiaffrino (Munich) |
Planar Quantum A-Infinity Algebras |
| |
abstract forthcoming... |
| June 8 |
Ingmar Saberi (Heidelberg) |
Holomorphic field theories and higher symmetries |
| |
abstract forthcoming... |
| June 15 |
N.N. |
TBA |
| |
abstract forthcoming... |
| June 22 |
Simone Noja (Milano) |
On Some Global and Local Problems in Supergeometry |
| |
abstract forthcoming... |
| June 29 |
Alberto Cattaneo (Zurich) |
Hamilton-Jacobi and Quantum Chern-Simons on Cylinders |
| |
A quantum field theory on a cylinder (“time” interval x “space”) is an evolution operator. Semiclassically it
is given by (the exponential of) the Hamilton-Jacobi action, i.e., the action functional evaluated on the
solution with the given initial and final “positions.” In the functional integral formalism, this is easily
obtained by observing that one can expand around such a solution. For gauge theories in the BV formalism,
however, this expansion is incompatible with a correct splitting of the bulk BV and the boundary BFV fields.
In this case, as we will show in several examples, the Hamilton-Jacobi action is recovered from the lowest-order
Feynman graphs. In this talk I will focus on Chern-Simons theories. In this case, as for every topological
field theory, the evolution operator on the quantization of the reduced phase space is, projectively, the
identity operator, so the only important information is a phase, which we will prove to be the Hamilton-Jacobi
action by dint of the above method. Actually, we work perturbatively before reduction, so there are even more
interesting terms. Moreover, one can play this game with a variety of different polarizations. Among the
results, gauged Wess-Zumino-Witten naturally arises from 3d nonabelian Chern-Simons theory with complex
polarizations and the Kodaira-Spencer action from 7d abelian Chern-Simons theory with a Calabi-Yau boundary
(and appropriate linear-nonlinear polarizations on the boundary components). The latter result was obtained
semiclassically by Shatashvili and Gerasimov. In our approach there is a choice of quantization for which
there are no further corrections. This talk is based on work in progress with Pavel Mnev and Konstantin
Wernli. |
| July 6 (cancelled) |
Francesca Ferrari (Trieste) |
Quantum modularity of 3-manifold invariants |
| |
Recently, a new homological invariant of 3-manifolds - which categorifies the Witten-Reshetikhin-Turaev
invariant - has been discovered. This is known as the homological block. In this talk, I will explain the
importance of quantum modular forms in the study of 3-manifold invariants and describe, in particular,
how to predict topological data of 3-manifolds via the quantum modular properties of the associated
homological block. The talk will be based on the article 1809.10148 and work in progress with Cheng,
Chun, Feigin, Gukov, and Harrison. |
| July 13 |
Thomas Creutzig (Alberta) |
Algebraic blow-up |
| |
I will introduce a novel translation functor for W-algebras. W-algebras are related via the AGT-correspondence
to four dimensional gauge theories and instanton partition functions of the gauge theories enjoy blow-up
equations. I will explain that the translation functor provides a derivation of these blow-up equations
from a W-algebra perspective. Moreover there are many more algebraic blow-up equations that should also
have a geometric interpretation.
|
| July 20 |
Thorsten Schimmanek (Wien) |
The quantum geometry of genus one fibered Calabi-Yau threefolds |
| |
The talk will consist of three parts.
First we are going to review basic notions from topological string theory on general Calabi-Yau threefolds,
most notably Gopakumar-Vafa invariants, the stringy Kähler moduli space and topological B-branes.
In the second part we are then equipped to discuss the beautiful relation between the enumerative geometry
of genus one fibered Calabi-Yau threefolds, certain auto-equivalences of the associated brane categories
as well as the theory of weak Jacobi forms.
Finally, we will describe how a particular subset of the enumerative invariants encodes the structure
of the fibration and classical techniques from mirror symmetry can be applied to determine the types of
reducible fibers.
If time permits, we will discuss an example where the corresponding physics via F-theory can then
be used to identify transitions to singular Calabi-Yau threefolds with enumerative geometry related to
\(\Gamma(2)\). |
| Date |
Speaker |
Title, Abstract |
| September 16 |
Vivek Singh (Warschau) |
Chern-Simons invariants, Multi-boundary Entanglement and Knot-Quiver Correspondence |
|
First, I will give a brief introduction to knot theory and its
connection to Chern-Simons quantum field theory. Then I will briefly
review my research works and particular focus on the recent
developments on entanglement entropy associated with multi-boundary
link complements. My plan to highlight the interesting relationship
between the volume of hyperbolic link complements to non-zero
entanglement negativity. In the end, I will briefly discuss
Knot-Quiver correspondence. |
Wednesday, October 2
Hörsaal, 2 p.m. |
Mauricio Romo (Beijing) |
Enumerative invariants from exponential networks |
| |
I will review some aspects of exponential networks associated to CY 3-folds described
by conic bundles. In particular I will focus on the relation between exponential networks and the so-called
nonabelianization map which serves as a tool to connect counting of 3d-5d BPS states with certain classes
of generalized DT invariants. |
| October 14 |
N.N. |
TBA |
| |
abstract forthcoming |
| October 21 |
Andrew Bruce (Luxemburg) |
(Z2)n-manifolds: recent developments and ongoing work |
| |
A locally ringed space approach to coloured supermanifolds was
recently initiated by Grabowski and Poncin together with a collection of
collaborators. We must comment that the theory, while a natural extension of
the theory of supermanifolds, is not always straightforward nor trivial. While
the basic ideas are now in place, we will report on some recent developments in
the general theory. I will then discuss applications of (Z2)n-manifolds to mixed
symmetry tensors as found in string theory.
|
October 28
(Philosophenweg) |
Alex Altland (Köln) |
TBA |
| |
abstract forthcoming |
| November 4 |
N.N. |
TBA |
| |
abstract forthcoming |
| November 11 |
N.N. |
TBA |
| |
abstract forthcoming |
| December 16 |
Paul Norbury (Melbourne/München) |
Enumerative geometry via the moduli space of super Riemann surfaces |
| |
It was conjectured by Witten and proven by Kontsevich that a generating function for intersection
numbers on the moduli space of curves is a tau function of the KdV hierarchy, now known as the Kontsevich-Witten
tau function. Mirzakhani reproved this theorem via the study of Weil-Petersson volumes of moduli spaces of
hyperbolic surfaces. In this lecture I will describe another collection of intersection numbers on the moduli
space of curves whose generating function is a tau function of the KdV hierarchy. The proof uses an analogue
of Mirzakhani's argument applied to the moduli space of super Riemann surfaces due to recent work of Stanford
and Witten. This appearance of the moduli space of super Riemann surfaces to solve a problem over the classical
moduli space is deep and surprising. |
Tuesday, January 7
2:30pm, SR 2 |
Sara Tukachinsky (IAS) |
Defining open Gromov-Witten invariants via Fukaya
\( A_\infty \) algebras |
| |
Given a symplectic manifold \(X\), let \(L\) be a Lagrangian submanifold. A Fukaya
\(A_\infty\) algebra associated with \(L\) is a deformation of the dg algebra of smooth differential forms
on \(L\) by pseudoholomorphic disks. This language turns out to be useful in open Gromov-Witten theory,
as demonstrated in joint works with Jake Solomon. In particular, we develop a way of defining disk-counting
invariants and show that they satisfy some general properties. For the projective space \((X,L)=({\mathbb C\mathbb P}^n,
{\mathbb R\mathbb P}^n)\),
these properties are sufficient to calculate all invariants explicitly.
No prior knowledge of the notions above will be assumed. |
Wednesday, January 8
11:15am, SR 9 |
Sara Tukachinsky (IAS) |
Quantum product on relative cohomology |
| |
The quantum product on the cohomology of a symplectic manifold X is a deformation of the cup product,
or wedge product in the de Rham model. The deformation is given by adding contributions from
pseudoholomorphic spheres. Adding a Lagrangian submanifold L, one might consider the relative
cohomology \(H^*(X,L)\). In a joint work with Jake Solomon, we define a quantum product on
\(H^*(X,L)\) that combines deformations of the wedge products of differential forms on \(X\) and \(L\),
with corrections coming from pseudoholomorphic spheres as well as disks with boundary conditions in
\(L\). The associativity of this product is equivalent to the open WDVV equations, a PDE in the generating
functions of the closed and open Gromov-Witten invariants.
|
| January 13 |
Pierrick Bousseau (ETH Zürich) |
Quasimodular forms from Betti number |
| |
This talk will be about refined curve counting on local P2, the noncompact Calabi-Yau 3-fold total space of the canonical line bundle of the projective plane. I will explain how to construct quasimodular forms starting from Betti numbers of moduli spaces of one-dimensional coherent sheaves on P2. This gives a proof of some stringy predictions about the refined topological string theory of local P2 in the Nekrasov-Shatashvili limit. Partly based on work in progress with Honglu Fan, Shuai Guo, and Longting Wu. |
Thursday, February 6
2:15pm, SR 5 |
Francesca Carocci (Edinburgh) |
Donaldson-Thomas invariants from numbers to MMHM (and back) |
| |
Donaldson-Thomas (DT) invariants were first introduced by Donaldson and Thomas as an enumerative theory for the Hilbert scheme of curves in Calabi-Yau 3-folds. In the past 20 years, they have been generalised and refined in various ways. In this talk, we concentrate on the DT invariants, first considered by Katz, arising from the mathematical incarnation of the moduli space of D-branes supported on curves. I will explain how these invariants are expected to be related to the genus 0 Gromov-Witten invariants, and then talk about a possible way to prove such a relation passing from numerical to categorical DT invariants. The latter will be a good excuse to talk about BPS Lie algebras for quiver with potentials and their use in DT theory.
|
| Date |
Speaker |
Title, Abstract |
| March 18 |
Luca Battistella (Bonn) |
Reduced Gromov-Witten theory in genus one and singular curves |
|
The moduli space of genus 0 stable maps to projective space is a
smooth orbifold. The quantum hyperplane principle allows us to compute the invariants
of a hypersurface as twisted invariants of projective space, hence e.g. by torus
localisation. In higher genus the moduli space can be arbitrarily singular. The
genus 1 case has been particularly studied: J. Li, R. Vakil, and A. Zinger have
desingularised the main component, defined reduced invariants, and compared them
with standard ones, providing the first mathematical proof of the BCOV mirror
symmetry prediction. Ten years later, we understand their construction in terms
of log geometry and singular (worse than nodal) curves, thanks to work of
D. Ranganathan, K. Santos-Parker, and J. Wise. I will describe some results in
this direction, jointly obtained with F. Carocci and C. Manolache, and N. Nabijou
and D. Ranganathan. |
Tuesday, April 23
Hörsaal, 2 p.m. |
Martin Cederwall (Göteborg) |
Pure spinors and supersymmetry |
| |
I will describe how pure spinors, suitably defined, arise from traditional superspace.
In cases of maximal supersymmetry, such as D=10 super-Yang-Mills theory and D=11 supergravity,
pure spinor superspace solves the old problem with off-shell formulations, and gives Batalin-Vilkovisky actions.
I will also mention some related applications of pure spinors and minimal orbits. |
| April 29 |
N.N. |
T.B.A. |
|
abstract forthcoming
|
| May 6 |
Xujia Chen (Stony Brook) |
Bounding chains for Welschinger's
invariants |
|
abstract forthcoming |
| May 13 |
no seminar |
T.B.A. |
|
abstract forthcoming |
| May 20 |
Francesca Ferrari (Trieste) |
False Theta Functions, Log VOA's and 3-Manifold Invariants |
|
Since the 1980s, the study of invariants of 3-dimensional manifolds has benefited
from the connections between topology, physics and number theory. Recently, a new topological
invariant that categorifies the Witten-Reshetikhin-Turaev invariant has been discovered. This is
known as the homological block. When the 3-manifold is a Seifert manifold given by a negative-definite
plumbing the homological block turned out to be related to false theta functions and characters
of logarithmic VOA's. In this talk, I describe the relations between this topological invariant,
certain number theoretical objects and the representation theory of logarithmic VOA's. |
Tuesday, May 21
Philosophenweg 19, 2pm |
Du Pei (Aarhus/Caltech) |
Taming the Non-Unitary Zoo with Wild Higgs Bundles |
|
We propose a new link between the geometry of moduli spaces of Higgs bundles and
quantum topology. The construction goes through a class of four-dimensional quantum field theories
that are said to satisfy "property F". Each such theory gives rise to a family of modular tensor
categories, whose algebraic structures are intimately related to the geometry of the Coulomb branch.
This is based on joint work with Mykola Dedushenko, Sergei Gukov, Hiraku Nakajima and Ke Ye. |
Tuesday, June 4
Hörsaal, 2pm |
Marc-Antoine Fiset (Oxford) |
Interpolating stringy geometry:
from Spin(7) and G2 to Virasoro N=2 |
|
Spectral flow, topological twists, chiral rings related to a refinement
of the de Rham cohomology and to marginal deformations, spacetime supersymmetry, mirror
symmetry. These are some examples of features arising from the N=2 Virasoro chiral
algebra of superstrings compactified on Calabi-Yau manifolds. To various degrees of
certainty, similar features were also established for compactifications on 7- and
8-dimensional manifolds with exceptional holonomy group \(G_2\) and Spin(7)
respectively. In this talk, I will explain that these are more than analogies:
I will flesh out the underlying symmetry connecting exceptional holonomy to
Calabi-Yau surfaces (K3) via a limiting process. |
| June 10 |
No Seminar (Whit Monday) |
| June 17 |
Ezra Getzler (Northwestern) |
The Batalin-Vilkovisky formalism and supersymmetric particles I |
|
Recently, I have been studying one-dimensional toy models of the superstring within the BV
formalism: these are known respectively as the spinning particle (analogous to the GSO superstring) and the
Superparticle (analogous to the Green-Schwarz superstring). The spinning particle turns out to be an AKSZ model,
and exhibits some very interesting pathologies: it appears to be the first model to have been investigated that
exhibits BV cohomology in all negative degrees.
By contrast, the superparticle has a very well-behaved BV cohomology. The action for the superparticle contains
a term of topological type (the dimensional reduction of a super-WZWN term), and to handle this, we borrow some ideas
from Sullivan's approach to rational homotopy theory.
In my third talk, I will turn to quantization: I will show how to generalize Lagrangians in the BV formalism to
"flexible Lagrangians", defined chart-by-chart with families of homotopies on the intersections of charts.
The work on the superparticle is joint with my graduate student Sean Pohorence. |
Tuesday, June 18
SR 00. 200, 2pm |
Ezra Getzler (Northwestern) |
The Batalin-Vilkovisky formalism and supersymmetric particles II |
|
Recently, I have been studying one-dimensional toy models of the superstring within the BV
formalism: these are known respectively as the spinning particle (analogous to the GSO superstring) and the
superparticle (analogous to the Green-Schwarz superstring). The spinning particle turns out to be an AKSZ
model, and exhibits some very interesting pathologies: it appears to be the first model to have been investigated
that exhibits BV cohomology in all negative degrees.
By contrast, the superparticle has a very well-behaved BV cohomology. The action for the superparticle contains a term
of topological type (the dimensional reduction of a super-WZWN term), and to handle this, we borrow some ideas from
Sullivan's approach to rational homotopy theory.
In my third talk, I will turn to quantization: I will show how to generalize Lagrangians in the BV formalism to
"flexible Lagrangians", defined chart-by-chart with families of homotopies on the intersections of charts.
The work on the superparticle is joint with my graduate student Sean Pohorence. |
Wednesday, June 19
SR 9, 9am ct |
Ezra Getzler (Northwestern) |
The Batalin-Vilkovisky formalism and supersymmetric particles III |
|
Recently, I have been studying one-dimensional toy models of the superstring within the BV
formalism: these are known respectively as the spinning particle (analogous to the GSO superstring) and the
superparticle (analogous to the Green-Schwarz superstring). The spinning particle turns out to be an AKSZ model,
and exhibits some very interesting pathologies: it appears to be the first model to have been investigated that
exhibits BV cohomology in all negative degrees.
By contrast, the superparticle has a very well-behaved BV cohomology. The action for the superparticle contains a term of
topological type (the dimensional reduction of a super-WZWN term), and to handle this, we borrow some ideas from Sullivan's
approach to rational homotopy theory.
In my third talk, I will turn to quantization: I will show how to generalize Lagrangians in the BV formalism to "flexible
Lagrangians", defined chart-by-chart with families of homotopies on the intersections of charts.
The work on the superparticle is joint with my graduate student Sean Pohorence. |
Wednesday, August 21
SR 3, 2 p.m. |
Alexey Basalaev (Skoltech) |
Open WDVV equation and ADE singularities F-manifolds |
|
abstract forthcoming |
| Date |
Speaker |
Title, Abstract |
Tuesday, March 13
2:00 p.m.s.t. |
Piotr Kucharski (Uppsala) |
Extremal \(A\)-polynomials of knots |
|
In my talk, I will explain in an elementary way what extremal \(A\)-polynomials are,
and show how to obtain them from the usual (\(a\)-deformed) \(A\)-polynomials of knots. Then I will
try to reward your attention by showing applications in knot theory, string theory, and contact geometry. |
Friday, March 16
SR 3, 2:00 p.m.s.t. |
Piotr Kucharski (Uppsala) |
Knots–Quivers Correspondence |
|
This is a continuation of Piotr's previous talk, which will focus on recent work with
Sułkowski, Reinecke, and Stošić. |
Monday, July 9
SR C, 2:00 p.m.s.t. |
Eric Sharpe (Virginia) |
A proposal for nonabelian mirrors in two-dimensional theories |
|
In this talk we will describe a proposal for nonabelian mirrors to two-dimensional \((2,2)\)
supersymmetric gauge theories, generalizing the Hori-Vafa construction for abelian gauge theories.
Specifically, we will describe a construction of B-twisted Landau-Ginzburg orbifolds whose classical
physics encodes Coulomb branch relations (quantum cohomology), excluded loci, and correlation functions
of A-twisted gauge theories. The proposal has been checked in a wide variety of cases, but the talk
will focus on exploring the proposal in two examples: Grassmannians (constructed as \({\it U}(k)\) gauge
theories with fundamental matter), and SO(2k) gauge theories. If time permits, we will also discuss
how this mirror proposal can be applied to test and refine recent predictions for IR behavior of pure
supersymmetric \({\it SU}(n)\) gauge theories in two dimensions. |
Monday, July 16, 2pm
Philosophenweg 19! |
Michael Gutperle (UCLA) |
Holographic description of 5-dimensional conformal field
theories. |
|
This is the abstract. |
Wednesday, August 8
SR 3, 2:00 p.m.s.t. |
Makiko Mase (Tokyo Metropolitan University) |
On duality of families of K3 surfaces |
|
Since an introduction to mathematical world from physicians, many concepts of
mirror symmetry has been studied. In my talk, we will discuss a mirror of polytopes due to Batyrev,
and that of Picard lattices of families of K3 surfaces due to Dolgachev. We conclude that
these mirror symmetries correspond when we consider families that are obtained by a strange
duality of bimodal singularities due to Ebeling-Takahashi, and Ebeling-Ploog. |
| 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 four-manifolds using BPS spectra of
quantum field theories. While most of them are completely novel, some of
the new invariants categorify well-known old invariants such as the WRT
invariant of 3-manifolds and the Donaldson invariant of 4-manifolds. 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 half-BPS 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 half-index. Using the half-index as a guide, we
study the actions of a variety of 3d dualities on the boundary
conditions, including level-rank duality, mirror symmetry, and
Seiberg-like 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
better-known wall-crossing! -- 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 |
|
Number-theorists 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 Chern-Simons 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
Calabi-Yau manifold match Lagrangian submanifolds of the mirror dual
Calabi-Yau. 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 Calabi-Yau 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 6-manifold. |
| February 19 |
Guglielmo Lockhart (Amsterdam) |
Universal features of 6d self-dual 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, self-dual 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 self-dual 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 self-duality 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 well-approximated 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.
|
| Date |
Speaker |
Title, Abstract |
| April 10 |
Ingmar Saberi (Heidelberg) |
Holographic lattice field theories |
|
Recent developments in tensor network models (which are, roughly speaking, quantum circuits
designed to produce analogues of the ground state in a conformal field theory) have led to
speculation that such networks provide a natural discretization of the AdS/CFT correspondence.
This raises many questions: just to begin, is there any sort of lattice field theory model
underlying this connection? And how much of the usual AdS/CFT dictionary really makes sense
in a discrete setting? I'll describe some recent work that proposes a setting in which such
questions can perhaps be addressed: a discrete spacetime whose bulk isometries nevertheless
match its boundary conformal symmetries. Many of the first steps in the AdS/CFT dictionary
carry over without much alteration to lattice field theories in this background, and one
can even consider natural analogues of BTZ black hole geometries.
|
Tuesday, April 11
2 p.m.s.t. |
Michael Gekhtman (Notre Dame) |
Higher pentagram maps via cluster mutations and networks on surfaces
|
|
The pentagram map that associates to a projective polygon a new one formed by
intersections of short diagonals was introduced by R. Schwartz and was shown to
be integrable by V. Ovsienko, R. Schwartz and S. Tabachnikov. M. Glick
demonstrated that the pentagram map can be put into the framework of the theory
of cluster algebras, a new and rapidly developing area with many exciting
connections to diverse fields of mathematics. In this talk I will explain that
one possible family of higher-dimensional generalizations of the pentagram map
is a family of discrete integrable systems intrinsic to a certain class of
cluster algebras that are related to weighted directed networks on a torus and a
cylinder. After presenting necessary background information on Poisson geometry
of cluster algebras, I will show how all ingredients necessary for integrability
- Poisson brackets, integrals of motion - can be recovered from combinatorics of
a network. The talk is based on a joint project with M. Shapiro, S. Tabachnikov
and A. Vainshtein.
|
| May 29 |
Jon Keating (Bristol) |
The Riemann hypothesis
and physics — a perspective |
|
I will give an overview of some connections, mostly
speculative, between the Riemann Hypothesis, random matrix theory, and
quantum chaos. |
| July 3 |
Alex Turzillo (Caltech) |
Spin TQFT and fermionic gapped phases |
|
I will discuss state sum constructions of two-dimensional Spin TQFTs and
their G-equivariant generalizations. These models are related to tensor network descriptions
of ground states of fermionic topological matter systems. We will revisit the classification
of fermionic short range entangled phases enriched by a finite symmetry G and derive a group
law for their stacking. |
| July 10 |
Markus Banagl (Heidelberg) |
Intersection homology and
the conifold transition |
|
Abstract forthcoming |
| Date |
Speaker |
Title, Abstract |
| November 28 |
John Alexander Cruz Morales (Bonn) |
On Stokes matrices for Frobenius manifolds |
|
In this talk we will discuss how to compute the Stokes matrices for some semisimple Frobenius manifolds
by using the so-called monodromy identity. In addition, we want to discuss the case when we get integral
matrices and their relations with mirror symmetry. This is part of an ongoing project with M. Smirnov
and previous joint work with Marius van der Put.
|
| December 5 |
Adam Alcolado (McGill) |
Extended Frobenius Manifolds |
|
Frobenius manifolds, introduced by Dubrovin, are objects which know about many different things in
mathematics, for example, the enumeration of rational curves, or the list of platonic solids. We
will introduce a generalization of Frobenius manifolds which know about real (or open) enumerative
geometry. What else do these extended Frobenius Manifolds know?
|
| December 12 |
Pietro Longhi (Uppsala) |
Probing the geometry of BPS states with spectral networks |
|
In presence of defects the Hilbert space of a quantum field theory can change in
interesting ways. Surface defects in 4d N=2 theories introduce a class of 2d-4d
BPS states, which the original 4d theory does not possess. For theories of class
S, spectral networks count 2d-4d BPS states, and through the 2d-4d wall-crossing
phenomenon the 4d BPS spectrum can be obtained. Adopting this physical viewpoint
on spectral networks, I will illustrate some recent and ongoing developments
based on this framework, with applications to the study of 2d (2,2) BPS spectra,
and of 4d N=2 BPS monodromies.
|
| Tuesday, December 13 |
Michael Bleher (Heidelberg) |
Supersymmetric Boundary Conditions in
N=4 Super Yang-Mills Theory |
|
In the last decade it was realized that supersymmetric boundary conditions in super Yang-Mills
theories can provide invaluable insight into several areas of current mathematical research.
Motivated especially by their appearance in a categorification of knot invariants, I will give
a short overview on half-BPS boundary conditions in 4d N=4 SYM theory. Of particular interest
is the Nahm-pole boundary condition and the main goal will be to review the corresponding moduli
space of supersymmetric vacua.
|
| January 30 |
Chris Elliott (IHÉS) |
Algebraic Structures for Kapustin-Witten
Twisted Gauge Theories |
|
Topological twisting is a technique for producing topological field theories from supersymmetric
field theories -- one exciting application is Kapustin and Witten's 2006 discovery that the categories
appearing in the geometric Langlands conjecture can be obtained as topological twists of N=4 supersymmetric
gauge theories, and that these two categories are interchanged by S-duality. There are, however, several
incompatibilities between Kapustin and Witten's construction and the geometric representation theory
literature. First, their techniques do not produce the right algebraic structures on the moduli
spaces appearing in geometric Langlands, and secondly, their construction doesn't explain the singular
support conditions Arinkin and Gaitsgory introduced in order to make the geometric Langlands
correspondence possible. In this talk I'll explain joint work with Philsang Yoo addressing both
of these issues: how to understand topological twisting in (derived) algebraic geometry, and
how to interpret singular support conditions as arising from the choice of a vacuum state.
|
Wednesday, February 1
SR B, 2 p.m.s.t. |
Chris Elliott (IHÉS) |
An Introduction to the Batalin-Vilkovisky Quantization Formalism |
|
Abstract forthcoming
|
| February 13 |
Steven Sivek (Bonn) |
The augmentation category of a Legendrian knot |
|
Given a Legendrian knot in R3, Shende, Treumann, and Zaslow defined a
category of constructible sheaves on the plane with singular support controlled by the
front projection of the knot. This category turns out to be equivalent to a unital
A∞ category, called the augmentation category, which is defined in terms of a
holomorphic curve invariant (Legendrian contact homology) of the knot.
In this talk I will describe the construction of these categories and outline a proof that
they are equivalent. This is joint work with Lenny Ng, Dan Rutherford, Vivek Shende,
and Eric Zaslow.
|
| February 20 |
Ben Knudsen (Harvard) |
A local-to-global approach to configuration spaces |
|
I will describe how ideas borrowed from functorial field theory,
the theory of chiral algebras, and BV theory may be profitably adapted to
the purely topological problem of calculating Betti numbers of
configuration spaces. These methods lead to improvements of classical
results, a wealth of computations, and a new and combinatorial proof of
homological stability.
|
| February 27 |
Owen Gwilliam (Bonn) |
Chiral differential
operators and the curved beta-gamma system |
|
Chiral differential operators (CDOs) are a vertex algebra analog
of the associative algebra of differential operators. They were originally
introduced by mathematicians using just sheaf theory and vertex algebraic
machinery. Later, Witten explained how CDOs on a complex manifold X arise
as the perturbative part of the curved beta-gamma system with target X. I
will describe recent work with Gorbounov and Williams in which we construct
the BV quantization of this theory and use a combination of factorization
algebras and formal geometry to recover CDOs. At the end, I hope to discuss
how the techniques we developed apply to a broad class of nonlinear sigma
models, including source manifolds of higher dimension.
|
| March 20 |
Michele Cirafici (I.S.T. Lisboa) |
Framed BPS quivers and line defects |
|
I will discuss a certain class of line defects in four dimensional supersymmetric theories
with N=2. I will show that many properties of these
operators can be rephrased in terms of quiver representation theory. In
particular one can study BPS invariants of a new kind, the so-called framed BPS
states, which correspond to bound states of ordinary BPS states with the defect.
I will discuss how these invariants arise from framed quivers. Time permitting I
will also discuss a formalism to study these quantities based on cluster
algebras.
|
| Date |
Speaker |
Title, Abstract |
| April 25 |
Zhentao Lu (Oxford) |
Quantum sheaf cohomology on Grassmannians |
|
I will give a brief introduction to quantum sheaf cohomology and correlation functions. I will
talk about the computation of the classical cohomology ring \(\sum H^q(X, \wedge^p E^*)\) for a
vector bundle \(E\) over the Grassmannian \(X\), also known as the polymology. Then I will talk
about the conjectural quantum sheaf cohomology derived from the Coulomb branch argument of
the physics theory of gauged linear sigma models. |
| May 2 |
Seung-Joo Lee (Virginia Tech) |
Witten Index for Noncompact Dynamics |
|
Many of the gauged dynamics motivated by string theory come with gapless asymptotic directions. In this
talk, we focus on d=1 GLSM's of such kind and their Witten indices, having in mind of the associated D-brane
bound state problems. Upon illustrating by examples that twisted partition functions can be misleading,
we proceed to explore how physical Witten indices can sometimes be embedded therein. There arise
further subtleties when gapless continuum sectors come from a gauge multiplet, as in non-primitive quiver
or pure Yang-Mills theories. For such theories, the twisted partition functions tend to involve fractional
expressions. We point out that these are tied to the notion of rational invariant in the wall-crossing
formulae, offering a general mechanism of extracting the Witten index directly from the twisted partition
function.
|
May 12
Thursday, 2pm, SR 11 |
Satoshi Nawata (Caltech/Aarhus) |
Various formulations of knot homology |
|
This lecture is preceded by a talk entitled
"Knot Homology from String Theory" in the
Oberseminar Conformal field theory
on Wednesday May 11, 2pm, Philosophenweg 12 |
| May 23 |
N.N. |
T.B.A. |
| June 13 |
Nicolò Piazzalunga (Trieste/Madrid) |
Real Topological String Theory |
June 23
Thursday, 2pm
RZ Statistik 02.104 |
Matt Young (Hong Kong) |
Algebra and geometry of orientifold Donaldson-Thomas theory |
|
I will give an overview of the orientifold Donaldson-Thomas theory of quivers. Roughly speaking,
orientifold Donaldson-Thomas theory is a virtual counting theory for principal G-bundles
in three dimensional Calabi-Yau categories, where G is an orthogonal or symplectic group.
This theory is best formulated in terms of geometrically defined representations of cohomological
Hall algebras. I will explain how this set-up leads naturally to a categorification of the orientifold
wall-crossing formula appearing in the string theory literature, a proof of the orientifold variant of
the integrality conjecture of Kontsevich-Soibelman and a geometric interpretation of orientifold
Donaldson-Thomas invariants. Partially based on joint work with Hans Franzen (Bonn).
|
| July 11 |
N.N. |
T.B.A. |
| July 25 |
Mauricio Romo (IAS) |
Complex Chern-Simons and cluster algebras |
|
I'll describe the cluster partition function (CPF), a computational tool that uses elements from
algebra and representation theory to describe the partition function of Chern-Simons theory with
gauge group SL(N,C) given some prescribed boundary conditions. The CPF allows for a perturbative
expansion that can be used to compute invariants of a large class of hyperbolic knots. I'll comment on
its relation with M-theory and further applications such as insertion of line operators, if time allows.
|
| Date |
Speaker |
Title |
| October 20 |
Thomas Reichelt (Heidelberg) |
Semi-infinite Hodge structures. An introduction |
| November 2 |
N.N. |
T.B.A. |
| November 16 |
Dominik Wrazidlo (Heidelberg) |
Positive Topological Quantum Field Theories and Fold Maps |
| December 7 |
Dmytro Shklyarov (Chemnitz) |
On an interplay between Hodge theoretic and categorical invariants of singularities |
| December 14 |
Cornelius Schmidt-Colinet (München) |
Conformal perturbation defects between 2d CFTs |
|
We consider some examples and properties of interfaces implementing
renormalisation group flows between two-dimensional conformal field theories, including general
perturbative results for entropy and transmissivity, and the explicit constructions for flows
between coset models.
|
January 11
INF 227 (KIP) SB1.107 |
Renato Vianna (Cambridge) |
Infinitely many monotone Lagrangian tori in del Pezzo surfaces |
|
In 2014, we showed how the Chekanov torus arises as a fiber of an
almost toric fibration and how this perspective enables us to describe an
infinite range of monotone Lagrangian tori. More precisely, for any Markov
triple of integers \((a,b,c)\) -- satisfying \(a^2+b^2+c^2=3abc\) -- we get a
monotone Lagrangian torus \(T(a^2,b^2,c^2)\) in \({\mathbb C} P^2\). Using
neck-stretching techniques we are able to get enough information on the
count of Maslov index \(2\) pseudo-holomorphic disks that allow us to show
that for \((d,e,f)\) a Markov triple distinct from \((a,b,c)\), \(T(d^2,e^2,f^2)\)
is not Hamiltonian isotopic to \(T(a^2,b^2,c^2)\).
In this talk we will describe how to get almost toric fibrations for all
del Pezzo surfaces, in particular for \({{\mathbb C} P}^2{\#{k{\overline{{{\mathbb C}P}^2}}}}\)
for \(4\le k\le 8\), where there is no toric fibrations (with monotone symplectic
form). From there, we will be able to construct infinitely many monotone
Lagrangian tori. Some Markov like equations appear. They are the same as the
ones appearing in the work of Haking-Porokhorov regarding degeneration
of surfaces to weighted projective spaces.
|
| January 18 |
N.N. |
T.B.A. |
| January 25 |
Penka Georgieva (Jussieu) |
Real Gromov-Witten theory in all genera |
|
We construct positive-genus analogues of Welschingers invariants for many real
symplectic manifolds, including the odd-dimensional projective spaces and the quintic threefold.
Our approach to the orientability problem is based entirely on the topology of real bundle pairs
over symmetric surfaces. This allows us to endow the uncompactified moduli spaces of real maps
from symmetric surfaces of all topological types with natural orientations and to verify that
they extend across the codimension-one boundaries of these spaces. In reasonably regular cases,
these invariants can be used to obtain lower bounds for counts of real curves of arbitrary genus.
Joint work with A. Zinger.
|
| February 1 |
N.N. |
T.B.A. |
