Organized by Kenji Fukaya, Dusa McDuff, and John Morgan
January 2 – June 30, 2014
GromovWitten theory, LagrangianFloer homology and symplectic field theory arise from the notion of pseudoholomorphic curves, possibly with boundary conditions, in symplectic manifolds. All these theories rely in a fundamental way on Gromov’s compactness result for moduli spaces of pseudoholomorphic curves, as well as on results about gluing and transversality. A central issue is how to use these analytic results in various contexts to produce appropriate structures on the moduli spaces, structures that allow one to define a virtual fundamental cycle that can then be used to produce algebraic invariants.
The program will focus on two basic approaches to understanding the structure of these moduli spaces:
(1) local finitedimensional models derived from the local Kuranishi obstruction picture, and
(2) infinite dimensional analysis — the polyfold approach.
The purpose of this program is to examine foundational analytic and topological questions associated with these approaches, especially in key examples such as the closed case (GromovWitten theory), Hamiltonian and LagrangianFloer theory and contact homology. The aim is to compare and contrast the approaches with each other and with alternative methods, such as those in algebraic geometry or those provided by Joyce’s derived smooth manifold theory.
Speaker and Seminar Schedule:
The weekly talks take place on Tuesdays at 11:15am and 2:30pm (beginning January 21) in room 313.
Dusa McDuff will host a minicourse on Kuranishi Atlases, Thursdays at 11:45am in the Simons Center for Geometry and Physics Seminar Room, 313. More details about these lectures can be found here: http://scgp.stonybrook.edu/scientific/minicourses/minicoursebydusamcduffkuranishiatlases
Kenji Fukaya will host a minicourse on Kuranishi Structures, Fridays at 12:00pm in the Simons Center for Geometry and Physics Seminar Room, 313. More details about these lectures can be found here: http://mysbfiles.stonybrook.
Katrin Wehrheim is hosting an online course on Regularization of Moduli Spaces of Pseudholomorphic Curves. All videos, notes and live stream can be accessed here: http://scgp.stonybrook.edu/scientific/minicourses/regularizationofmodulispacesofpseudholomorphiccurveskatrinwehrheim
Date and Time  Title  Presenters  
1/21 at 11:15am – Room 313  Lifted Floer homology and topology of monotone Lagrangian submanifolds  Mihai Damian  Video 
1/21 at 2:30pm – Room 313  Some remarks on hydrodynamic stability  Kai Cieliebak  Video NA due to inclement weather 
1/28 at 11:15am – Room 313  Minimal Discrepancy of Isolated Singularities and Reeb Orbits  Mark McLean  Video 
1/28 at 2:30pm – Room 313  Cylindrical contact homology as a welldefined homology?  Joanna Nelson  Video 
1/31 at 12:00pm – Room 313  Virtual fundamental chain, pseudoholomorphic curve and Kuranishi structure  Kenji Fukaya  More Details / Video 
2/4 at 11:15am – Room 313  Minimal Discrepancy of Isolated Singularities and Reeb Orbits Continued  Mark McLean  Video 
2/4 at 2:15pm – Room 313  Cylindrical contact homology as a sometimes welldefined homology  Joanna Nelson  Video 
2/6 at 11:45am – Room 313  Kuranishi Atlases  Dusa McDuff  More Details / Video 
2/7 at 12:00pm – Room 313  Virtual fundamental chain, pseudoholomorphic curve and Kuranishi structure  Kenji Fukaya  More Details / Video 
2/11 at 2:30pm – Room 313  Length and volume in SeibergWitten theory  Daniel CristofaroGardiner  Video 
2/14 at 12:00pm – Room 313  Cancelled  Kenji Fukaya  More Details 
2/18 at 11:15am – Room 313  Minimal Discrepancy of Isolated Singularities and Reeb Orbits Continued  Mark McLean  Video 
2/18 at 2:30pm – Room 313  On Floer cohomology and nonarchimedian geometry  Mohammed Abouzaid  Video 
2/20 at 11:45am – Room 313  Kuranishi Atlases  Dusa McDuff  More Details / Video 
2/21 at 12:00pm – Room 313  Virtual fundamental chain, pseudoholomorphic curve and Kuranishi structure  Kenji Fukaya  More Details / Video 
2/25 at 11:15am – Room 313  Transversality via the Donaldson hypersurface technique – Part 1  Klaus Mohnke  Video / Notes 
2/25 at 2:30pm – Room 313  Kuranishi Atlases  Dusa McDuff  More Details 
2/28 at 12:00pm – Room 313  Virtual fundamental chain, pseudoholomorphic curve and Kuranishi structure  Kenji Fukaya  More Details / Video 
MARCH
3/4 at 11:15am – Room 313  Transversality via the Donaldson hypersurface technique – Part 2  Klaus Mohnke  Video / Notes 
3/4 at 2:30pm – Room 313  Analysis of contact CauchyRiemann maps and canonical connection on contact manifolds, I  Rui Wang  Video 
3/6 at 11:45am – Room 102  Introduction to virtual neighborhood technique  Bohui Chen  Video 
3/7 at 12:00pm – Room 313  Virtual fundamental chain, pseudoholomorphic curve and Kuranishi structure  Kenji Fukaya  Video 
3/11 at 11:15am – Room 313  Transversality via the Donaldson hypersurface technique – Part 3  Klaus Mohnke  Video 
3/11 at 2:30pm – Room 313  Analysis of contact CauchyRiemann maps and canonical connection on contact manifolds, II  YongGeun Oh  Video 
3/13 at 11:45am – Room 102  Seminar Series on Kuranishi Atlases  Dusa McDuff  More Details / Video 
3/14 at 12:00pm – Room 313  Seminar Series on Kuranishi Structures  Kenji Fukaya  Video 
3/25 at 11:15am – Room 313  GW invariants relative normal crossing divisors  Eleny Ionel  Video 
3/25 at 2:30pm – Room 313  GW invariants relative normal crossing divisors  Eleny Ionel  Video 
3/28 at 12:00pm – Room 313  Seminar Series on Kuranishi Structures  Kenji Fukaya  Video 
4/1 at 11:15am – Room 313  Towards Viterbo functoriality for nonexact Liouville embeddings  Janko Latschev  Video 
4/3 at 11:45am – Room 313  Seminar Series on Kuranishi Atlases: The role of additivity  Dusa McDuff  More Details / Video 
4/4 at 12:00pm – Room 313  Seminar Series on Kuranishi Structures  Kenji Fukaya  Video 
4/8 at 11:15am – Room 313  Looking for flexibility in higherdimensional contact manifolds  Olga Plamenevskaya  Video 
4/10 at 11:45am – Room 313  Seminar Series on Kuranishi Atlases  Dusa McDuff  More Details / Video 
4/11 at 12:00pm – Room 313  Seminar Series on Kuranishi Structures  Kenji Fukaya  Video 
4/15 at 2:30pm – Room 313  Cyclic homology in Toric A LandauGizburg B Mirror symmetry  Kenji Fukaya  Video 
4/17 at 11:45am – Room 313  Seminar Series on Kuranishi Atlases  Dusa McDuff  More Details / Video 
4/18 at 12:00pm – Room 313  Seminar Series on Kuranishi Structures  Kenji Fukaya  Video 
4/22 at 2:30pm – Room 313  Periodic Symplectic Cohomologies  Jingyu Zhao  Video 
4/24 at 11:45am – Room 313  Seminar Series on Kuranishi Atlases  Dusa McDuff  More Details / Video 
4/25 at 12:00pm – Room 313  Seminar Series on Kuranishi Structures  Kenji Fukaya  Video 
4/29 at 11:00am – Room 313  Absolute vs Relative GromovWitten Invariants  Aleksey Zinger  Video 
4/29 at 2:30pm – Room 313  Absolute vs Relative GromovWitten Invariants  Aleksey Zinger  Video 
5/20 at 11:15am – Room 313  The Lagrangian Cubic Equation  Paul Biran  Video 
5/27 at 2:30pm – Room 313  Category of Kuranishi structure germs and a forgetful functor from polyfold Fredholm sections  Dingyu Yang  Video 
6/10 at 2:30pm – Room 313  Cyclic homology and S^1equivariant symplectic cohomology  Sheel Ganatra  Video 
6/16 at 11:15am – Room 313  Applications and computations of contact homology revisited  Frederic Bourgeois  
6/16 at 2:00pm – Room 313  Obstruction bundle gluing in cylindrical contact homology  Michael Hutchings  
6/17 at 11:15am – Room 313  Symplectic and contact differential graded algebras  Alex Oancea  
6/17 at 2:00pm – Room 313  TBA  Mohammed Abouzaid  
6/18 at 11:15am – Room 313  Two approaches to S^1equivariant symplectic homology  Frederic Bourgeois  
6/18 at 2:00pm – Room 313  Transversality for multiple covers  Chris Wendl  
6/19 at 11:15am – Room 313  Transversality for S^1equivariant symplectic homology  Alex Oancea  
6/19 at 2:00pm – Room 313  Daniel ChristofaroGardiner 
Additional information:
– Workshop on Moduli Spaces of Pseudoholomorphic Curves I occurs from March 17 – 21, 2014. Please see the workshop webpage here: http://scgp.stonybrook.edu/archives/7149
– There will be joint seminar series by Helmut Hofer and Dominic Joyce May 5 – 9, 2014. More details can be found HERE
– A workshop on Equivariant GromovWitten Theory and Applications occurs from May 12 – 16, 2014. Please see the workshop webpage here: http://scgp.stonybrook.edu/archives/7153
– Workshop on Moduli Spaces of Pseudoholomorphic Curves II occurs from June 2 – 6, 2014. Please see the workshop webpage here: http://scgp.stonybrook.edu/archives/7151
– There will be an informal workshop on the foundations of contact homology from June 16 – 20, 2014.
]]>Organized by Alexander Abanov, Dmitri Kharzeev, Boris Khesin, Dam Son, and Paul Wiegmann
February 17June 13, 2014
Recent developments in relativistic hydrodynamics place it at the crossroads of nuclear physics, condensed matter physics and string theory. Hydrodynamics is known to be very effective in describing the longwavelength behavior of many body systems regardless of the strength of interparticle interactions. It encapsulates general conservation laws and symmetries of the system.
Quantum anomalies can break some of the symmetries of the underlying theory. While it was known for a long time that anomalies induce observable effects in quantum field theories, only quite recently it has become clear that anomalies also have important macroscopic manifestations and affect transport and hydrodynamics — in particular, anomalies make possible nondissipative transport and bring to the existence novel collective excitations. The effects of anomalies are especially important in the systems that possess chiral fermions (e.g. quantum Hall systems, graphene or quarkgluon plasma) and where topologically nontrivial configurations are present (e.g. vortices, skyrmions or sphalerons).
An important advantage of hydrodynamics is that it is formulated explicitly in terms of physical observables. Therefore, the hydrodynamical approach usually leads directly to the predictions for the experiment, both in condensed matter and nuclear physics. Furthermore, topological methods in hydrodynamics could shed some light on the search for new symmetries related to quantum anomalies. Topological fluid dynamics is a young branch of mathematics which studies group symmetries of various equations of hydrodynamical origin, as well as geometric and topological properties of their solutions and of the corresponding magnetic and vortex fields. The interaction of the relativistic and topological approaches in hydrodynamics might also lead to new insights into the turbulence and singularity problems.
The goal of the program is to develop hydrodynamic descriptions in condensed matter physics and QCD at finite temperature and density with an emphasis on the effects of quantum anomalies and topology. Among these effects is the nondissipative transport of charges and energy — with a wide range of applications in science and technology, from quantum computing to the detection of topological fluctuations of QCD in heavy ion collisions. We aim at advancing quantum hydrodynamics through the use of topological and geometric methods.
Speaker and Seminar Schedule:
The weekly talks take place on Mondays at 4pm (beginning Monday January 27) and Thursdays at 1:00pm (beginning Thursday January 16) in room 313.
Date and Time  Title  Presenters  
1/16 at 1:00pm – Room 313  Intro: Holographic fluids and superfluids  Tigran Kalaydzhyan  More Details 
1/23 at 10:30am – Room 313  Chiral anomaly, kinetic theory, and the Chiral Magnetic/Vortical Effect  Gökçe Basar  More Details 
1/27 at 4:00pm – Room 313  Relativistic Hydrodynamics in the presence of Anomalies  Gustavo Monteiro  More Details 
1/30 at 10:30am – Room 313  An Introduction to Holographic Superconductivity  Chris Herzog  More Details 
2/10 at 4:00pm – Room 313  Chiral and Gravitational Anomalies on Fermi surfaces  Ismail Zahed  More Details 
2/17/14 – 2/21/14  WORKSHOP: Quantum Anomalies and Hydrodynamics: Applications to Nuclear and Condensed Matter Physics  More Details  
2/24/14 – 2/28/14  WORKSHOP: Strongly Coupled Systems Away From Equilibrium  More Details  
3/6 at 1:00pm – Room 313  Quantum Lax pair for the deformed CalogeroMoser systems  Alexander Veselov  More Details 
3/10 at 4:00pm – Room 313  Deriving anomalyinduced response from thermal equilibrium  Kristan Jensen  More Details 
3/17 at 4:00pm – Room 313  Anomalous Zero Sound  Alexander Gorsky  More Details 
3/20 at 1:00pm – Room 313  Deriving anomalyinduced response from thermal equilibrium. Part II  Kristan Jensen  More Details 
3/24 at 2:00pm – YITP Common Room 6125 
Momentum Dissipation and Charge Transport in Holograpy

Richard Davison

YITP Seminar 
3/27 at 1:00pm – Room 313  Lorentz invariance in chiral kinetic theory  Mikhail Stephanov  More Details 
3/31 at 4:00pm – Room 313  Torus knot invariants from Calogero model  Ksenia Bulycheva  More Details 
4/3/14 at 1:00pm – Room 313  Thermal Corrections to Entanglement Entropy for Conformal Field Theory  Chris Herzog  More Details 
4/7/14 at 4:00pm – Room 313  Chiral superfluidity in QCD  Tigran Kalaydzhyan  More Details 
4/10/14 at 2:30pm – Room 313  The role of anomaly inflow in the theory of chiral quantum fluids  Juerg Froehlich  More Details 
4/14/14 at 4:00pm – Room 313  Q&A seminar: Loewner evolution and integrable systems  Alexander Vasiliev  More Details 
4/21/14 at 4:00pm – Room 313  Quantum Hall effect and Kähler metrics 
Semyon Klevtsov

More Details 
4/22/14 at 1:00pm – Room 102  Fractional Quantum Hall Effect on Riemann Surfaces  Paul Wiegmann  More Details 
4/24/14 at 1:00pm – Room 313  Towards experimental characterisation of topological order at a fractional quantum Hall edge  Vadim Cheianov  More Details 
4/28/14 at 4:00pm – Room 313  Quantum Hydrodynamics of Weyl Fermions  Dmitri Kharzeev  More Details 
5/1/14 at 1:00pm – Room 313  Holography and Equilibration  Edward Shuryak  More Details 
5/5/14 at 4:00pm – Room 313  On the generating functional in dissipative hydrodynamics  Pavel Kovtun  More Details 
5/6/14 at 2:30pm – Room 102  Quantum impurity problems and conformal field theory  Ian Affleck  More Details 
5/7/14 at 2:30pm – YITP Common Room 6125  Topological Superconductor – Luttinger liquid Junctions  Ian Affleck  More Details 
5/8/14 at 1:00pm – Room 313  Spectral theory of periodic triangular difference operators and its applications  Igor Krichever  More Details 
5/12/14 at 4:00pm – Room 313  Exact Solutions to the NavierStokes Equations  Oleg Bogoyavlenskij  More Details 
5/13/14 at 4:00pm – Room 313  A universal correction to higher spin entanglement entropy  Justin David  More Details 
5/14/14 at 1:00pm – Room 313  Controlling quantum flux through measurement: an idealised example  Denis Bernard  More Details 
5/15/14 at 1:00pm – Room 313  Critical phenomena in weakly dispersive nonlinear Hamiltonian PDEs and universality  Boris Dubrovin  More Details 
5/19/14 – 5/23/14  WORKSHOP: Geometrical Aspects of Hydrodynamics  More Details  
5/27/14 at 1:00pm – Room 313 
Stability of twodimensional topological insulators  Andrea Cappelli  More Details 
5/29/14 at 1:00pm – Room 313 
Casimir Effect: Diffraction and general boundary conditions  Dimitra Karabali  More Details 
6/5/14 at 10:30am – Room 313 
OPE in statistical mechanics – what is it good for?  Alexander Zamolodchikov  More Details 
6/9/14 at 4:00pm – Room 313 
Maxwell Electrodynamics on 4 torus as a topologically ordered system  Ariel Zhitnitsky  More Details 
Organized by Ljudmila Kamenova, Alexander Kirillov, Jr., Nikita Nekrasov, and Olivier Schiffmann
September 30 – November 8, 2013
Quivers and quiver varieties, introduced and studied in a series of papers of Nakajima, Lusztig, Ringel and others in 1990s, have since appeared in many areas of mathematics and mathematical physics, from gauge theory, string theory, noncommutative geometry to geometric representation theory to geometry. They were instrumental in the geometric constructions of Lie algebras and their representations.
This program will cover some of the most important applications of quiver varieties. It will be divided into 3 concentration periods, each running for 2 weeks
– Quiver Varieties and physics (gauge theory, BPS/CFT correspondence, and the AGT conjecture in particular): Sept 30 – Oct 11.
– Representation theory (Hall algebras, geometric construction of Lie algebras…): Oct 14 – Oct 25
– Complex geometry (moduli spaces of instantons, monopoles, etc.): Oct 28 – Nov 8
The emphasis of the program will be to bring together people from different fields and encouraging informal interactions among them.
Speaker and Seminar Schedule:
The weekly seminars will take place on Tuesday at 2:30pm in room 313 (unless otherwise specified below).
Date and Time  Title  Presenters  
10/1 at 2:30pm – Room 102  Bethe states as defects in gauge theories  Nikita Nekrasov  
10/3 at 2:30pm – Room 313  N=2 gauge theories and quiver representations  Sergio Cecotti  
10/8 at 1:00pm – Room 102  Representation theory and gauge theory  Hiraku Nakajima  
10/8 at 2:30pm – Room 313  Hilbert series of Coulomb branch for N=2 dimension 3 field theory  Amihay Hanany  
10/10 at 1:00pm – Room 102  Introduction to quiver gauge theories  Nikita Nekrasov  
10/11 at 11:00am – Room 313  Mirror Symmetry in 3d N=2 Quiver Gauge Theories  Peter Koroteev  
10/22 at 2:30pm – Room 313  Refined knot invariants and Hilbert schemes  Eugene Gorsky  
10/23 at 11:00am – Room 313  Representations of quivers with loops  Tristan Bozec  
10/30 at 10:00am – Room 313  Hamiltonian local models for symplectic derived stacks  Chris Brav 
ASSOCIATED VIDEOS
Physics and Mathematics of Scattering Amplitudes
Organized by Zvi Bern, Lance Dixon, Michael Douglas, Alexander Goncharov, and Lionel Mason
Fall 2013
Starting date: August 26, 2013
The study of scattering amplitudes in relativistic quantum field theory has undergone a remarkable renaissance and transformation in recent years, with the advent of new perturbative approaches such as generalized unitarity, recursion relations, twistor variables and topological string theory, colorkinematics duality and doublecopy properties. Scattering in N=4 superYangMills theory, a highly supersymmetric cousin of QCD, can be described, in the planar limit of a large number of colors, in terms of minimal surfaces in antide Sitter space. This approach has also led to a remarkable correspondence between scattering amplitudes and polygonal Wilson loops, and to discovery of new symmetries such as dual conformal invariance and Yangian symmetry. The intricate structure of string theory scattering amplitudes is also rapidly being uncovered.
Powerful mathematical notions are rapidly playing important roles, including the (positive) Grassmanian and polytopes, (motivic) multiple zeta values, singlevalued multiple (harmonic) polylogarithms, and the symbol of an iterated integral. Other ideas, such as integrability and the OPE expansion, have appeared but are still awaiting full exploitation.
Some of these ideas have had practical payoff within perturbative QCD, for the computation of more accurate cross sections at the LHC. Many of them are the most powerful, or at least best understood, for planar N=4 superYangMills theory. Due to its large symmetry, this theory can serve as a proving ground for new ideas and approaches. It holds the promise of being exactly solvable, yet it will still require more physical and mathematical insights to fulfill this promise. Other methods can be applied to gravitational theories, in particular the most supersymmetric pointlike theory of gravity, N=8 supergravity, where they have exposed remarkably good ultraviolet behavior at the multiloop level.
Speaker and Seminar Schedule:
The weekly talks take place Tuesdays and Thursdays at 11:00am in room 313.
Date and Time  Title  Presenters  
8/29 at 11:00am – Room 313  Basics of Scattering Amplitudes  Henriette Elvang  
8/30 at 3:00pm – Room 313  From Feynman integrals to polylogarithms  Johannes Henn  
9/10 at 11:00am – Room 313  Superconformal invariance for amplitudes and correlation functions  Emery Sokatchev  
9/13 at 11:00am – Room 313  Unexpected relations between YangMills and gravity amplitudes  Donal O’Connell  
9/17 at 1:00pm – Room 102  The Amplituhedron  Nima Arkani Hamed  
9/18 at 11:00am – Room 313  Unexpected relations between amplitudes and correlation functions  Paul Heslop  
9/18 at 2:00pm – Room 313  Graphical Functions  Oliver Schnetz  
9/19 at 11:00am – Room 313  TBA  Alexander Zhiboedov  
9/24 at 11:00am – Room 313  Hodge structures and PicardFuchs equations in perturbative QFT  Stefan Weinzeriel  
9/24 at 4:00pm – Harriman 137  Harmony of Scattering Amplitudes: From Quantum Chromodynamics to Supergravity  Zvi Bern  
9/26 at 11:00am – Room 313  Twistors, gravity, and amplitudes  Timothy Adamo  
10/1 at 11:00am – Room 313  SpaceTime Smatrix and FluxTube Smatrix  Pedro Viera  
10/3 at 11:00am – Room 313  Polylogarithms and cluster coordinates in N=4 scattering amplitudes  Cristian Vergu  
10/8 at 11:00am – Room 313  Amplitudes and the Elliptic dilogarithm: physics and arithmetic of the sunset diagram in two dimensions  Pierre Vanhove  
10/10 at 11:00am – Room 313  Generalized Unitarity at One and Two Loops  Jacob Bourjaily  
10/15 at 11:00am – Room 313  Radu Roiban  
10/17 at 11:00am – Room 313  Hexagon Functions: Bootstrapping the ThreeLoop Remainder Function  Matt von Hippel  
10/22 at 11:00am – Room 313  Fundamental representation colorkinematics duality and N<4 supergravity  Henrik Johansson  
10/23 at 11:00am – Room 313  MuellerNavelet Jets, SingleValued Harmonic Polylogarithms and Multiple Zeta Values  Lance Dixon  
10/24 at 11:00am – Room 313  On Yangian Symmetry of Scattering Amplitudes  Niklas Beisert  
10/28 at 2:00pm – Room 313  Scattering amplitudes in string theory and Eisenstein series  Michael Green and Stephan Miller  
10/29 at 11:00am – Room 313  Introduction to cluster algebras and the positive Grassmannian  Lauren Williams  
10/30 at 11:30am – Room 313  Physics and Combinatorics of the Grassmannian  Nima ArkaniHamed and Alexander Postnikov  
11/5 at 11:00am – Room 313  Two topics in infrared behavior  George Sterman  
11/7 at 11:00am – Room 313  Scattering of Massless Particles in Arbitrary Dimension  Song He  
11/12 at 11:00am – Room 313  BCJ numerators at one–loop from the superstring: Five points and beyond  Oliver Schlotterer  
11/14 at 11:00am – Room 313  Motivic Superstring Amplitudes  Stephan Stieberger  
11/19 at 11:00am – Room 313  Multiple polylogarithms in weight 4  Herbert Gangl  
12/5 at 11:00am – Room 313  Yangian Symmetry of smooth Wilson Loops in N=4 SYM  Jan Plefka  
12/6 at 11:00am – Room 313  Supergravity in a brilliant disguise  Tomasz Taylor 
ASSOCIATED VIDEOS AND PUBLICATIONS
]]>Organized by Miranda Cheng, Matthias Gaberdiel, and Terry Gannon
August 26 – September 27, 2013
Modular functions, Jacobi forms and mock modular forms appear naturally in various contexts in string theory and conformal field theory. In particular, characters of conformal field theories (CFTs) define (vectorvalued) modular functions, while Jacobi forms and mock modular forms arise from the elliptic genus of superstring compactifications. For example, the Jfunction is the character of the famous Monster CFT, while the unique weak Jacobi form of weight zero and index one, φ0,1, is the elliptic genus of the superstring compactification on a K3 surface.
About 30 years ago, it was noted that the Fourier coefficients of the Jfunction can be interpreted in terms of representations of the Monster group, the largest simple sproadic finite group, and this gave rise to a development that is now usually referred to as `Monstrous Moonshine’. A few years ago, Eguchi, Ooguri and Tachikawa (EOT) made a similar observation regarding φ0,1: they noted that its Fourier coefficients can be interpreted in terms of representations of M24representations, where M24 is the largest Mathieu group, another simple sporadic finite group. Moreover, this observation has a nice formulation in terms of the mock modular form that is naturally associated to φ0,1.
While the conjecture of EOT has by now been largely established, there are many intriguing open questions that remain. For example, while the Monster CFT provided a microscopic explanation of at least some aspects of Monstrous Moonshine, none of the superstring theories on K3 actually possess M24 as their automorphism group. Moreover, intriguing extensions of the EOT conjecture to higher index weak Jacobi forms (umbral moonshine) and generalisations to situations with less supersymmetry have recently been found, but the proper context in which all of these observations fit remains to be understood. In this program, we hope to bring together experts from different areas, including vertex operator algebra, string theory, algebraic geometry and number theory, in order to make progress with these very topical problems.
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