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VERSION:2.0
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BEGIN:VEVENT
SUMMARY:Meromorphic connections and quivers
DTSTART;VALUE=DATE-TIME:20160627T103000Z
DTEND;VALUE=DATE-TIME:20160627T105500Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153248@indico.cern.ch
DESCRIPTION:Speakers: Daisuke Yamakawa (Tokyo Institute of Technology)\nIn
this talk I will review recent developments on the relationship between m
eromorphic connections on the Riemann sphere and quivers. Such relationshi
p was first found by Crawley-Boevey in the case of logarithmic connections
. He used it to solve the additive Deligne-Simpson problem\, a sort of exi
stence problem on logarithmic connections. I will explain the generalizati
on of Crawley-Boevey's result conjectured by Boalch and solved affirmative
ly by Hiroe and myself\, and touch on related topics.\n\nhttps://indico.ce
rn.ch/event/375104/contributions/2153248/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153248/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Welcome address
DTSTART;VALUE=DATE-TIME:20160627T072000Z
DTEND;VALUE=DATE-TIME:20160627T072500Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153252@indico.cern.ch
DESCRIPTION:https://indico.cern.ch/event/375104/contributions/2153252/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153252/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Physics and Mathematics for the End of Spacetime
DTSTART;VALUE=DATE-TIME:20160702T133000Z
DTEND;VALUE=DATE-TIME:20160702T143000Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153323@indico.cern.ch
DESCRIPTION:Speakers: Nima Arkani-Hamed (IAS\, Princeton)\nhttps://indico.
cern.ch/event/375104/contributions/2153323/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153323/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cohomological Hall algebra actions and Kac polynomials
DTSTART;VALUE=DATE-TIME:20160628T093000Z
DTEND;VALUE=DATE-TIME:20160628T102000Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153277@indico.cern.ch
DESCRIPTION:Speakers: Olivier Schiffmann (Université de Paris-Sud\, Orsay
)\nWe consider cohomological Hall algebras associated to quivers and their
actions on the cohomology of Nakajima varieties\; we relate these algebr
as with the Yangians constructed by Maulik and Okounov\, and show that the
ir Hilbert series are encoded by the Kac polynomials of the underlying qui
ver. For instance\, for the 1-loop quiver\, one obtains the Yangian of $\\
widehat{gl(1)}$ used relevant in the study of the AGT conjecture on $P^2$.
We also speculate on what the analog of all this when the quiver gets rep
laced by a curve.\n\nhttps://indico.cern.ch/event/375104/contributions/215
3277/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153277/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hexagons and 3-point functions
DTSTART;VALUE=DATE-TIME:20160629T083000Z
DTEND;VALUE=DATE-TIME:20160629T085500Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153291@indico.cern.ch
DESCRIPTION:Speakers: Benjamin Basso (ENS Paris)\nI will present a framewo
rk for computing correlators of three single trace operators in planar N=4
SYM theory that uses hexagonal patches as building blocks. This approach
allows one to exploit the integrability of the theory and derive all loop
predictions for its structure constants. After presenting the main ideas a
nd results\, I will discuss recent perturbative tests and open problems. B
ased on [arXiv 1505.06745]\n\nhttps://indico.cern.ch/event/375104/contribu
tions/2153291/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153291/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catching monodromy
DTSTART;VALUE=DATE-TIME:20160702T091500Z
DTEND;VALUE=DATE-TIME:20160702T101500Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153320@indico.cern.ch
DESCRIPTION:Speakers: Andrei Okounkov (Columbia University)\nI will talk a
bout monodromy of special functions\, why is it important\, and about some
new ways in which mathematical physicists are learning to think about the
monodromy of special functions of interest.\n\nhttps://indico.cern.ch/eve
nt/375104/contributions/2153320/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153320/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quantum Geometry
DTSTART;VALUE=DATE-TIME:20160702T120000Z
DTEND;VALUE=DATE-TIME:20160702T130000Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153321@indico.cern.ch
DESCRIPTION:Speakers: Robbert Dijkgraaf (IAS\, Princeton)\nhttps://indico.
cern.ch/event/375104/contributions/2153321/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153321/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quantum Spectral Curve for AdS/CFT and its applications
DTSTART;VALUE=DATE-TIME:20160629T103000Z
DTEND;VALUE=DATE-TIME:20160629T105500Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153293@indico.cern.ch
DESCRIPTION:Speakers: Nikolai Gromov (King's College\, London )\nhttps://i
ndico.cern.ch/event/375104/contributions/2153293/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153293/
END:VEVENT
BEGIN:VEVENT
SUMMARY:3D supersymmetric gauge theories and Hilbert series
DTSTART;VALUE=DATE-TIME:20160628T083000Z
DTEND;VALUE=DATE-TIME:20160628T085500Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153274@indico.cern.ch
DESCRIPTION:Speakers: Stefano Cremonesi (King's college\, London)\nThe Hil
bert series is a generating function that enumerates gauge invariant chira
l operators of a supersymmetric field theory with four supercharges and an
R-symmetry. In this talk I will explain how the counting of dressed ‘t
Hooft monopole operators leads to a formula for the Hilbert series of a 3d
N=2 gauge theory\, which captures precious information about the chiral r
ing and the geometry of the moduli space of supersymmetric vacua of the th
eory.\n\nhttps://indico.cern.ch/event/375104/contributions/2153274/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153274/
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Chern character of the Verlinde bundle
DTSTART;VALUE=DATE-TIME:20160630T083000Z
DTEND;VALUE=DATE-TIME:20160630T085500Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153295@indico.cern.ch
DESCRIPTION:Speakers: Dimitri Zvonkine (Université Pierre et Marie Curie\
, Paris)\nThe Verlinde bundle\, or the bundle of conformal blocks\, is a v
ector bundle whose rank is given by the well-known Verlinde formula. We wi
ll explain how Teleman's classification of semi-simple cohomological field
theories allow one to find the Chern character of this vector bundle.\n\n
https://indico.cern.ch/event/375104/contributions/2153295/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153295/
END:VEVENT
BEGIN:VEVENT
SUMMARY:What is gravity ?
DTSTART;VALUE=DATE-TIME:20160702T080000Z
DTEND;VALUE=DATE-TIME:20160702T090000Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153319@indico.cern.ch
DESCRIPTION:Speakers: Hirosi Ooguri (Caltech)\nhttps://indico.cern.ch/even
t/375104/contributions/2153319/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153319/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reduction for SL(3) pre-buildings
DTSTART;VALUE=DATE-TIME:20160627T093000Z
DTEND;VALUE=DATE-TIME:20160627T102000Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153254@indico.cern.ch
DESCRIPTION:Speakers: Carlos Simpson (Université de Nice - Sophia Antipol
is)\nWe discuss some aspects of the reduction process leading to a pre-bui
lding associated to an SL(3) spectral curve. This construction is related
to harmonic maps and the WKB problem\, and has potential applications to t
he construction of stability conditions. This is joint work with Katzarkov
\, Noll and Pandit [arXiv:1503.00989]\, see also [arXiv:1311.7101]\n\nhttp
s://indico.cern.ch/event/375104/contributions/2153254/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153254/
END:VEVENT
BEGIN:VEVENT
SUMMARY:From the Hitchin component to opers
DTSTART;VALUE=DATE-TIME:20160630T143000Z
DTEND;VALUE=DATE-TIME:20160630T145500Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153307@indico.cern.ch
DESCRIPTION:Speakers: Olivia Dumitrescu (MPIM\, Bonn)\nGaiotto's conjectur
e (2014) is a particular construction of opers from Higgs bundles in one H
itchin component. The conjecture has been recently solved by a joint pape
r of Dumitrescu\, Fredrickson\, Kydonakis\, Mazzeo\, Mulase\, and Neitzke
(2016). In this talk\, I will present a holomorphic description of the lim
iting oper\, and its geometry. The importance of this correspondence\, in
particular the relation with the "quantum curve" of Dumitrescu - Mulase (
2013) will be discussed.\n\nhttps://indico.cern.ch/event/375104/contributi
ons/2153307/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153307/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Derivation of modular anomaly equation in compact elliptic Calabi-
Yau spaces
DTSTART;VALUE=DATE-TIME:20160627T153000Z
DTEND;VALUE=DATE-TIME:20160627T155500Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153268@indico.cern.ch
DESCRIPTION:Speakers: Minxin Huang (University of Science and Technology o
f China)\nModular anomaly have been discovered in topological string theor
y on elliptic Calabi-Yau spaces. We extend the derivation of genus zero an
omaly equation for non-compact cases in the literature to compact cases. F
or higher genus\, we derive the modular anomaly equation from BCOV holomor
phic anomaly equation. Based on [arXiv:1501.04891].\n\nhttps://indico.cern
.ch/event/375104/contributions/2153268/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153268/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geometric Langlands applications of boundary conditions for maxima
lly supersymmetric Yang Mills theory
DTSTART;VALUE=DATE-TIME:20160701T143000Z
DTEND;VALUE=DATE-TIME:20160701T152000Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2184399@indico.cern.ch
DESCRIPTION:Speakers: Davide Gaiotto (Perimeter Institute\, Waterloo)\nI w
ill discuss the properties of boundary conditions of maximally supersymmet
ric Yang Mills theory compactified on a Riemann surface. Depending on the
details of the compactification\, this produces BAA branes (i.e. complex L
agrangian submanifolds) or BBB branes (i.e. hyper-holomorphic sheaves)\nfo
r the two-dimensional sigma model in the Hitchin moduli space. I will disc
uss the map from four-dimensional boundary conditions to two-dimensional b
oundary conditions\nand the action of S-duality on the system. Mathematica
lly\, this construction provides collections of Geometric Langland dual pa
irs of objects.\n\nhttps://indico.cern.ch/event/375104/contributions/21843
99/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2184399/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Exact WKB analysis\, cluster algebras and Painlevé equations
DTSTART;VALUE=DATE-TIME:20160627T083000Z
DTEND;VALUE=DATE-TIME:20160627T085500Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153257@indico.cern.ch
DESCRIPTION:Speakers: Kohei Iwaki (University of Nagoya)\nIn the first par
t of the talk I’ll describe a joint work with Tomoki Nakanishi and expla
in how the Voros symbols in exact WKB analysis realize (generalized) clust
er variables. In the second part I’ll generalize the notion of the Voros
symbols to the Painlevé equations\, and discuss their applications.\n\nh
ttps://indico.cern.ch/event/375104/contributions/2153257/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153257/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Moduli spaces of holomorphic and meromorphic differentials
DTSTART;VALUE=DATE-TIME:20160630T073000Z
DTEND;VALUE=DATE-TIME:20160630T082000Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153294@indico.cern.ch
DESCRIPTION:Speakers: Rahul Pandharipande (ETH Zurich)\nI will discuss a n
ew moduli space of holomorphic/meromorphic differentials on Riemann surfac
es (joint work with G. Farkas) and propose connections between the fundame
ntal class to Pixton's formulas and Witten's r-spin class (joint work with
F. Janda\, A. Pixton\, and D. Zvonkine).\n\nhttps://indico.cern.ch/event
/375104/contributions/2153294/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153294/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Poisson-Lie T-duality
DTSTART;VALUE=DATE-TIME:20160701T103000Z
DTEND;VALUE=DATE-TIME:20160701T105500Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153315@indico.cern.ch
DESCRIPTION:Speakers: Pavol Severa (University of Geneva)\nI will give a r
eview of Poisson-Lie T-duality\, which is a non-Abelian generalization of
T-duality\, and explain it in terms of Chern-Simons theory and its general
izations (AKSZ models) with appropriate boundary conditions. Based on [arX
iv:1602.05126]\n\nhttps://indico.cern.ch/event/375104/contributions/215331
5/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153315/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Higgs bundles\, branes and applications
DTSTART;VALUE=DATE-TIME:20160630T133000Z
DTEND;VALUE=DATE-TIME:20160630T135500Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153308@indico.cern.ch
DESCRIPTION:Speakers: Laura Schaposnik (University of Illinois at Chicago)
\nWe shall begin the talk by first introducing Higgs bundles for complex L
ie groups and the associated Hitchin fibration\, and\nrecalling how to rea
lize Langlands duality through spectral data. We will then look at a natur
al construction of families of subspaces which give different types of bra
nes\, and explain how the topology of some of these branes can be describe
d by considering the spectral data. Finally\, we shall give some applicati
ons of the above approaches in relation to Langlands duality\, and represe
ntations of 3-manifolds. Some of the work presented during the talk is in
collaboration with David Baraglia (Adelaide) and Steve Bradlow (UIUC) and
Nigel Hitchin (Oxford).\n\nhttps://indico.cern.ch/event/375104/contributio
ns/2153308/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153308/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Correlation Functions in Superconformal Field Theories
DTSTART;VALUE=DATE-TIME:20160630T093000Z
DTEND;VALUE=DATE-TIME:20160630T102000Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153300@indico.cern.ch
DESCRIPTION:Speakers: Jaume Gomis (Perimeter Institute\, Waterloo)\nWe dis
cuss the exact computation of correlation functions of local operators in
the Coulomb branch in four-dimensional N=2 superconformal field theories.\
n\nhttps://indico.cern.ch/event/375104/contributions/2153300/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153300/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Analytical Approaches to Coalescing Binary Black Holes
DTSTART;VALUE=DATE-TIME:20160701T093000Z
DTEND;VALUE=DATE-TIME:20160701T102000Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153312@indico.cern.ch
DESCRIPTION:Speakers: Thibault Damour (IHES\, Bures sur Yvette)\nThe ratio
nale for interpreting the recently announced events\nof the Laser Interfer
ometer Gravitational-Wave Observatory (LIGO) as gravitational wave (GW) si
gnals emitted during the coalescence of two black holes is the excellent m
atch between these events and the corresponding theoretical predictions wi
thin General Relativity. We shall review the mix of analytical and numeric
al methods that led to predict in advance the precise shape of the wavefor
m emitted by coalescing binary black holes. In particular\, we shall prese
nt the basis of the Effective One-Body method which has been crucial in al
lowing one to compute the bank of 250 000 GW templates that has been used
to search coalescence signals\, and to measure the masses and spins of th
e coalescing black holes.\n\nhttps://indico.cern.ch/event/375104/contribut
ions/2153312/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153312/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A Vafa-Witten invariant for projective surfaces
DTSTART;VALUE=DATE-TIME:20160629T093000Z
DTEND;VALUE=DATE-TIME:20160629T102000Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153292@indico.cern.ch
DESCRIPTION:Speakers: Richard Thomas (Imperial College\, London)\nI will d
escribe joint work with Yuuji Tanaka. We define a Vafa-Witten invariant fo
r algebraic surfaces. For Fano and K3 surfaces\, a standard vanishing theo
rem means it reduces to (roughly speaking) the Euler characteristic of the
moduli space of sheaves on the surface. For general type surfaces there a
re other contributions\, which we calculate.\n\nhttps://indico.cern.ch/eve
nt/375104/contributions/2153292/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153292/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chern–Simons theory on S^3/G and topological strings
DTSTART;VALUE=DATE-TIME:20160630T150000Z
DTEND;VALUE=DATE-TIME:20160630T152500Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153303@indico.cern.ch
DESCRIPTION:Speakers: Gaétan Borot (MPIM\, Bonn)\nWe study the matrix mod
els repreenting (a piece of) SU(N) Chern-Simons partition function on quot
ients of S^3 by a finite group of isometries (these are the spherical Seif
ert manifolds). We show 1) that these partition functions have 1/N asympto
tic (by opposition to formal) expansion\, which is computed by the topolog
ical recursion of Eynard and Orantin for a suitable spectral curve and 2)
that the spectral curve is algebraic and can be constructed in relation wi
th ADE root systems (E8 being realized by the Poincare sphere). We also sh
ow by explicit (and complete for all cases except E8) checks that this spe
ctral curve is a specialization of the spectral curve of a relativistic AD
E Toda chain considered by Marshakov et al. and Williams. Relying on large
N transitions\, geometric engineering and correspondences between gauge t
heories and integrable systems\, this fits into a generalization of the Go
pakumar-Vafa conjecture to S^3/G. E.g.\, a correspondence between its CS i
nvariants and the Gromov-Witten invariants of a Calabi-Yau 3 fold X_{G}\,
with the interesting feature that X_{G} is non-toric when G is not abelian
.\n\nhttps://indico.cern.ch/event/375104/contributions/2153303/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153303/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Framed BPS States In Two And Four Dimensions
DTSTART;VALUE=DATE-TIME:20160627T073000Z
DTEND;VALUE=DATE-TIME:20160627T082000Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153244@indico.cern.ch
DESCRIPTION:Speakers: Gregory Moore (Rutgers University)\nThis talk has fo
ur parts. Part one reviews the derivation of the Kontsevich-Soibelman wall
-crossing formula for BPS degeneracies in four-dimensional theories with N
=2 supersymmetry using framed BPS states. This follows the papers [ArXiv:1
006.0146\,1008.0030]. I might also mention briefly a possible generalizati
on under discussion with T. Dimofte and D. Gaiotto. Motivated by this poss
ible generalization the next part turns to two-dimensional theories. Part
two reviews the theory of interfaces defined by families of superpotential
s in two-dimensional Landau-Ginzburg models with (2\,2) supersymmetry\, an
d how this leads to a categorification of both S-wall-crossing (of spectra
l network theory) and of the Cecotti-Vafa wall-crossing formula. This part
reviews some material from [ArXiv:1506.04087] (see [ArXiv: 1506.04086] fo
r a ``brief'' introduction.) Part three applies the material of part two t
o the formulation of knot homology proposed by Witten in [ArXix:1101.3216]
and developed by Gaiotto and Witten in [ArXiv:1106.4789]. Part three is b
ased on the recent PhD thesis of Dmitriy Galakhov. If time permits\, part
four reviews a mathematically completely well-defined formulation of vecto
r spaces of framed BPS states for arbitrary 't Hooft-Wilson line defects\,
valid in the semiclassical regime of arbitrary d=4 N=2 theories with a La
grangian formulation. Part four is based on [ArXiv:1512.08923] and ongoing
work with Daniel Brennan.\n\nhttps://indico.cern.ch/event/375104/contribu
tions/2153244/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153244/
END:VEVENT
BEGIN:VEVENT
SUMMARY:SUSY field theories and geometric Langlands: The other side of the
coin
DTSTART;VALUE=DATE-TIME:20160627T123000Z
DTEND;VALUE=DATE-TIME:20160627T132000Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153259@indico.cern.ch
DESCRIPTION:Speakers: Joerg Teschner (DESY\, Hamburg)\nInclusion of surfac
e operators leads to interesting generalisations of the correspondence dis
covered by Alday\, Gaiotto and Tachikawa between four-dimensional N=2 SUSY
field theories and conformal field theory. My goal will be to outline how
this generalisation is related to the geometric Langlands correspondence
and to a certain quantum generalisation of this correspondence. The result
ing picture has interesting relations both to the CFT-based approach to th
e geometric Langlands correspondence developed by Beilinson and Drinfeld\,
and to the gauge-theoretic approach of Kapustin and Witten\, offering the
perspective to integrate all these approaches into a unified picture.\n\n
https://indico.cern.ch/event/375104/contributions/2153259/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153259/
END:VEVENT
BEGIN:VEVENT
SUMMARY:What Chern-Simons theory assigns to a point ?
DTSTART;VALUE=DATE-TIME:20160628T153000Z
DTEND;VALUE=DATE-TIME:20160628T155500Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153288@indico.cern.ch
DESCRIPTION:Speakers: André Henriques (Oxford and Utrecht University)\nAc
cording the cobordism hypothesis (proposed by Baez-Dolan\, and proved by L
urie)\, an extended topological quantum field theory is fully determined b
y its value on the point. A natural question is then: does this classifica
tion theorem apply to the topological quantum field theories of physical i
nterest? And if yes\, what is then the value of those theories on a point
(the latter will then determine the whole theory\, by the cobordism hypoth
esis). In this talk\, we will propose answers to the questions “What doe
s Chern-Simons theory assign to a point?” and “What kind of mathematic
al object does Chern-Simons theory assign to a point?” The answer to the
first question is "representations of the based loop group"\; the answer
to the second question is "categorified von Neumann algebras".\n\nhttps://
indico.cern.ch/event/375104/contributions/2153288/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153288/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Umbral symmetry groups and K3 CFTs
DTSTART;VALUE=DATE-TIME:20160701T133000Z
DTEND;VALUE=DATE-TIME:20160701T135500Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153313@indico.cern.ch
DESCRIPTION:Speakers: Sarah Harrison (Harvard)\nUmbral moonshine is a conn
ection between mock modular forms and discrete symmetry groups which arise
as automorphisms of the Niemeier lattices\, the 24-dimensional unimodula
r lattices labeled by their ADE root systems. The first example of Umbral
moonshine was original discovered by Eguchi\, Ooguri\, Tachikawa when expa
nding the elliptic genus of a K3 surface into N=4 characters and seeing co
efficients which are sums of irreducible representations of the sporadic g
roup M_{24}. In recent work with Miranda Cheng\, we have suggested that al
l umbral symmetry groups may have some relation to K3 CFTs. On the other h
and\, a theorem of Gaberdiel\, Hohenegger\, and Volpato has shown that sym
metries of K3 CFTs can naturally be classified by elements of the group Co
nway_0\, the automorphism group of the Leech lattice\, which preserve a fo
ur-plane. In this talk we briefly review the aforementioned results\, and
discuss the extension of this theorem a) to singular CFTs\, in which case
the role of Conway_0 is naturally replaced by certain umbral groups\, and
b) when one takes worldsheet parity into account. Based on [ArXiv:1406.06
19\, 1512.04942]\, and work to appear with Miranda Cheng and Roberto Volpa
to\n\nhttps://indico.cern.ch/event/375104/contributions/2153313/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153313/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Resurgence and exact quantization via holomorphic Floer cohomology
DTSTART;VALUE=DATE-TIME:20160701T073000Z
DTEND;VALUE=DATE-TIME:20160701T082000Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153309@indico.cern.ch
DESCRIPTION:Speakers: Maxim Kontsevich (IHES)\nI will present a new perspe
ctive on Riemann-Hilbert correspondence and wall-crossing based on the con
siderations of Fukaya categories associated with a holomorphic symplectic
manifold and a possibly singular analytic Lagrangian subvariety. This fram
ework includes holonomic D-modules (for the case of cotangent bundles) on
the same footing as q-difference equations.\n\nhttps://indico.cern.ch/even
t/375104/contributions/2153309/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153309/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Derived equivalences from a duality of non-abelian GLSM's
DTSTART;VALUE=DATE-TIME:20160701T083000Z
DTEND;VALUE=DATE-TIME:20160701T085500Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153311@indico.cern.ch
DESCRIPTION:Speakers: Jørgen Rennemo (Oxford)\nJoint work with Ed Segal.
Producing examples of non-isomorphic varietes X and Y with equivalent deri
ved categories is in general hard. A technique involving LG models and var
iation of GIT stability has recently proved to be a powerful way of obtain
ing such examples. Kentaro Hori has proposed an duality between different
non-abelian gauged linear sigma models. One consequence of this duality is
the equivalence of the category of B-branes associated with the dual GLSM
's. We prove this predicted categorical equivalence. Combining this with t
he LG/VGIT techniques we can then find new examples of varieties X\, Y\, (
geometrically described as linear sections of Pfaffian varieties) which ha
ve equivalent (or closely related) derived categories. Joint work with Ed
Segal. For background\, see e.g. Addington\, Donovan\, Segal [arXiv:1401.3
661] and Hori [arXiv:1104.2853]\n\nhttps://indico.cern.ch/event/375104/con
tributions/2153311/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153311/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quantized Coulomb branches of 3d N=4 gauge theories and difference
operators
DTSTART;VALUE=DATE-TIME:20160628T073000Z
DTEND;VALUE=DATE-TIME:20160628T082000Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153272@indico.cern.ch
DESCRIPTION:Speakers: Hiraku Nakajima (RIMS\, Kyoto)\nIn [arXiv:1503.03676
\,1601.03586] (with Braverman and Finkelberg)\, I have proposed a mathemat
ical approach to define Coulomb branches of 3d N=4 SUSY gauge theories. It
is based on the homology group of a certain moduli space\, and has a natu
ral quantization by the equivariant homology group. For a quiver gauge the
ory\, the quantized Coulomb branch has an embedding into the ring of diffe
rence operators on the Lie algebra of the maximal torus of the gauge group
[arXiv:1604.03586]. We then discuss examples\, e.g.\, relation to Macdona
ld operators and cyclotomic rational Cherednik algebras\, which is a joint
work with Kodera (to appear).\n\nhttps://indico.cern.ch/event/375104/cont
ributions/2153272/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153272/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Spectral theory and topological strings
DTSTART;VALUE=DATE-TIME:20160628T123000Z
DTEND;VALUE=DATE-TIME:20160628T132000Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153314@indico.cern.ch
DESCRIPTION:Speakers: Marcos Marino (University of Geneva)\nI present a co
njectural correspondence between topological string theory on toric Calabi
-Yau manifolds\, and the spectral theory of certain trace class operators
on the real line\, in the spirit of large N dualities. The operators are o
btained by quantization of the algebraic curves which define the mirror ma
nifolds to the Calabi-Yau's. This conjecture can be regarded as a non-pert
urbative definition of topological string theory on these backgrounds. It
gives precise and explicit predictions for the Fredholm determinants of th
e corresponding operators\, providing in this way a new class of exactly s
olvable problems in spectral theory. In addition\, it leads to exact quant
ization conditions for cluster integrable systems. For a review see [ArXiv
:1506.07757]\n\nhttps://indico.cern.ch/event/375104/contributions/2153314/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153314/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monopoles\, Vortices\, and Vermas
DTSTART;VALUE=DATE-TIME:20160628T133000Z
DTEND;VALUE=DATE-TIME:20160628T135500Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153282@indico.cern.ch
DESCRIPTION:Speakers: Mathew Bullimore (Oxford)\nIn three-dimensional gaug
e theories\, monopole operators create and destroy vortices. I will explor
e this idea in the context of three-dimensional gauge theories with N=4 su
persymmetry in the presence of an omega background. This leads to a finite
version of the AGT correspondence\, involving an action of the quantized
Coulomb branch on the equivariant cohomology of vortex moduli spaces. (Wo
rk with T.Dimofte\, D.Gaiotto\, J.Hilburn\, & H-C.Kim)\n\nhttps://indico.c
ern.ch/event/375104/contributions/2153282/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153282/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Conformal constraints on defects
DTSTART;VALUE=DATE-TIME:20160630T103000Z
DTEND;VALUE=DATE-TIME:20160630T105500Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153301@indico.cern.ch
DESCRIPTION:Speakers: Abhijit Gadde (IAS\, Princeton)\nI will explore the
constraints imposed by conformal invariance on defects in a conformal fiel
d theory. Correlation function of a conformal defect with a bulk local ope
rator is fixed by conformal invariance up to an overall constant. This giv
es rise to the notion of defect expansion\, where the defect itself is exp
anded in terms of local operators. A correlator of two defect operators ad
mits a number of conformal cross-ratios depending on their dimensionality.
I will find the differential equation obeyed by the conformal block and s
olve them in certain special cases. [arXiv:1602.06354]\n\nhttps://indico.c
ern.ch/event/375104/contributions/2153301/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153301/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Period integrals of algebraic manifolds and their differential equ
ations
DTSTART;VALUE=DATE-TIME:20160629T073000Z
DTEND;VALUE=DATE-TIME:20160629T082000Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153289@indico.cern.ch
DESCRIPTION:Speakers: Shing-Tung Yau (Harvard)\nPeriod integrals are trans
cendental objects that play a central role in the study of algebraic manif
olds. They describe deformations of the manifold\, among other things\, an
d were originally studied by Euler\, Gauss\, and Riemann. In recent time\,
they also turn out to be very important in topological field theories\, a
nd in particular mirror symmetry. In this talk\, we explain a recent metho
d to study period integrals through differential equations\, and describe
a few applications including the resolution of some open issues.\n\nhttps:
//indico.cern.ch/event/375104/contributions/2153289/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153289/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Two mathematical applications of little string theory
DTSTART;VALUE=DATE-TIME:20160701T123000Z
DTEND;VALUE=DATE-TIME:20160701T132000Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153280@indico.cern.ch
DESCRIPTION:Speakers: Mina Aganagic (UC Berkeley)\nI will describe two mat
hematical applications of little string theory. The first leads to a varia
nt of AGT correspondence that relates q-deformed W-algebra conformal block
s to K-theoretic instanton counting. This correspondence can be proven for
any simply laced Lie algebra. The second leads to a variant of quantum La
nglands correspondence which relates q-deformed conformal blocks of an aff
ine Lie algebra and a W-algebra\, associated to a Langlands dual pair of L
ie groups. The proof of the correspondence for simply laced Lie algebras i
nvolves\, in a crucial way\, the recently discovered elliptic stable envel
opes.\n\nhttps://indico.cern.ch/event/375104/contributions/2153280/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153280/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elliptically fibered Calabi-Yau threefolds: mirror symmetry and Ja
cobi forms
DTSTART;VALUE=DATE-TIME:20160627T143000Z
DTEND;VALUE=DATE-TIME:20160627T152000Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153264@indico.cern.ch
DESCRIPTION:Speakers: Sheldon Katz (University of Illinois at Urbana-Champ
aign)\nI explain an ansatz for the partition function of elliptically fibe
red Calabi-Yau threefolds in terms of Jacobi forms using a combination of
B-model\, homological mirror symmetry\, and geometric techniques. This t
alk is based on joint work with Minxin Huang and Albrecht Klemm appearing
in [arXiv:1501.04891] as well as work in progress.\n\nhttps://indico.cern.
ch/event/375104/contributions/2153264/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153264/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Moduli spaces of curves with non-special divisors
DTSTART;VALUE=DATE-TIME:20160630T123000Z
DTEND;VALUE=DATE-TIME:20160630T132000Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153302@indico.cern.ch
DESCRIPTION:Speakers: Alexander Polischchuk (University of Oregon)\nIn thi
s talk I will discuss the moduli spaces of pointed curves with possibly no
n-nodal singularities such that the marked points form a nonspecial ample
divisor. I will show that such curves have natural projective embeddings\
, with a canonical choice of homogenous coordinates up to rescaling. Using
Groebner bases technique this leads to the identification of the moduli w
ith the quotient of an affine scheme by the torus action. These moduli spa
ces also have a natural interpretation in terms of the Krichever map. In t
he genus 1 case I will describe explicitly the corresponding GIT stability
conditions. If time allows\, I will explain how the same moduli spaces ap
pear when studying A-infinity algebras associated with curves. Based on \n
[arXiv:1511.03797\,1603.01238]\n\nhttps://indico.cern.ch/event/375104/cont
ributions/2153302/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153302/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Plane partitions and W algebras
DTSTART;VALUE=DATE-TIME:20160628T102000Z
DTEND;VALUE=DATE-TIME:20160628T104500Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153278@indico.cern.ch
DESCRIPTION:Speakers: Mikhail Bershtein (Landau Institute\, Moscow)\nI wil
l talk about new example of W algebras depending on three integer numbers
n\,m\,k. Category of representations of such algebras is equivalent (simil
ar to Drinfeld–Kohno or Kazhdan–Lusztig theorem) to the category of re
presentations of product of three quantum groups gl_{n|k}\, gl_{k|m} and g
l_{m|n}. Irreducible representations of these W algebras have a basis labe
led by plane partition with asymptotic conditions along three coordinate a
xes. Based on joint work with B. Feigin and G. Merzon [arXiv:1512.08779] a
nd work in progress.\n\nhttps://indico.cern.ch/event/375104/contributions/
2153278/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153278/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Higgs branches\, vertex operator algebras and modular differential
equations
DTSTART;VALUE=DATE-TIME:20160628T143000Z
DTEND;VALUE=DATE-TIME:20160628T152000Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153286@indico.cern.ch
DESCRIPTION:Speakers: Leonardo Rastelli (Stony Brook University)\nAny four
-dimensional N=2 superconformal field theory (SCFT) admits a subsector of
operators and observables isomorphic to a vertex operator algebra. After r
eviewing this correspondence (first identified in arXiv:1312.5344)\, I wil
l aim to characterize the relationship between the Higgs branch of the SCF
T (as an algebraic geometric object) and the associated vertex operator al
gebra. Our proposal is simple\, but its correctness requires the presence
of a number of null vectors in the vacuum Verma module of the algebra. One
null vector in particular leads to the prediction that the Schur index of
any N=2 SCFT should obey a modular differential equation and transform as
an element of a vector valued modular form. We illustrate these ideas in
a number of examples including a series of rank one theories associated wi
th ``Deligne's exceptional series'' of simple Lie algebras\, as well as a
number of Argyres-Douglas theories.\nReferences: Based on work with C. B
eem (to appear soon)\, building on the construction of arXiv:1312.5344 and
arXiv:1408.6522. For general background on N=2 superconformal field theor
ies in d=4\, see e.g. Tachikawa’s review arXiv:1312.2684. For background
on Zhu’s theory and the modular differential equations satisfied by VOA
s\, the original paper is Zhi\, J. Amer. Math Soc. 9 (1996)\, no. 1 237-30
2\, see e.g. Gaberdiel and Keller\, arXiv:0804.0489 (and references therei
n) for a review in the physics literature.\n\nhttps://indico.cern.ch/event
/375104/contributions/2153286/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153286/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fredholm determinant and Nekrasov type representations for isomono
dromic tau functions
DTSTART;VALUE=DATE-TIME:20160627T133000Z
DTEND;VALUE=DATE-TIME:20160627T135500Z
DTSTAMP;VALUE=DATE-TIME:20201204T075801Z
UID:indico-contribution-375104-2153260@indico.cern.ch
DESCRIPTION:Speakers: Oleg Lisovyy (LMPT\, Tours)\nWe will derive Fredholm
determinant representation for isomonodromic tau functions of Fuchsian sy
stems with $n$ regular singular points on the Riemann sphere and generic m
onodromy in $\\mathrm{GL}(N\,C)$. The corresponding operator acts in the d
irect sum of $N( n-3) $ copies of $L^2(S^1)$. Its kernel is expressed in t
erms of fundamental solutions of $n-2$ elementary 3-point Fuchsian systems
whose monodromy is determined by monodromy of the relevant $n$-point syst
em via a decomposition of the punctured sphere into pairs of pants. For $N
=2$ these building blocks have hypergeometric representations\, the kernel
becomes completely explicit and has Cauchy type. In this case Fredholm de
terminant expansion yields multivariate series representation for the tau
function of the Garnier system obtained earlier via its identification wit
h Fourier transform of Liouville conformal block (or a dual Nekrasov-Okoun
kov partition function). Further specialization to $n=4$ gives a series re
presentation of the general solution to Painlevé VI equation.\n\nhttps://
indico.cern.ch/event/375104/contributions/2153260/
LOCATION:Collège de France Amphithéâtre Marguerite de Navarre
URL:https://indico.cern.ch/event/375104/contributions/2153260/
END:VEVENT
END:VCALENDAR