Physics Around Mirror Symmetry

Conference Date: 
Lundi, Octobre 21, 2013 (All day) to Vendredi, Octobre 25, 2013 (All day)
Scientific Areas: 
Mathematical Physics

This conference will discuss recent developments in mirror symmetry, a subject at the intersection of leading developments in mathematics and physics and that been at the genesis of many developments in mathematical physics. 

The conference will bring together leading mathematicians and physicist to discuss the various very new approaches to the subject, that range from powerful physics based methods to new mathematical approaches.

Register for the conference HERE

  • Gaetan Borot, Max Planck Institute for Mathematics & MIT
  • Vincent Bouchard, University of Alberta
  • Ricardo Couso, University of Santiago de Compostela
  • Emanuel Diaconescu, Rutgers University
  • David Favero, University of Alberta
  • Davide Gaiotto, Perimeter Institute
  • Marco Gualtieri, University of Toronto
  • Kentaro Hori, Kavli IPMU
  • Shamit Kachru, Stanford University
  • Spiro Karigiannis, University of Waterloo
  • Albrecht Klemm, University of Bonn
  • Ilarion Melnikov, Albert Einstein Institute
  • Takuya Okuda, University of Tokyo
  • Callum Quigley, University of Alberta
  • Yan Soibelman, Kansas State University
  • Johannes Walcher, McGill University
  • Nikolay Bobev, Perimeter Institute
  • Gaetan Borot, Max Planck Institute for Mathematics & MIT
  • Vincent Bouchard, University of Alberta
  • Ricardo Couso, University of Santiago de Compostela
  • Emanuel Diaconescu, Rutgers University
  • Nima Doroud, Perimeter Institute
  • David Favero, University of Alberta
  • Sara Filippini, Fields Institute
  • Ilmar Gahramanov, Humboldt University
  • Davide Gaiotto, Perimeter Institute
  • Jaume Gomis, Perimeter Institute
  • Marco Gualtieri, University of Toronto
  • Kentaro Hori, Kavli IPMU
  • Shamit Kachru, Stanford University
  • Spiro Karigiannis, University of Waterloo
  • Albrecht Klemm, University of Bonn
  • Peter Koroteev, Perimeter Institute
  • Ilarion Melnikov, Albert Einstein Institute
  • Alex Molnar, Queens University
  • Ruxandra Moraru, University of Waterloo
  • Takuya Okuda, University of Tokyo
  • Peter Overholser, University of California, San Diego
  • Andrija Perunicic, Fields Institute
  • Callum Quigley, University of Alberta
  • Simon Rose, Fields Institute
  • Helga Ruddat, University of Mainz
  • Laura Schaposnik, University of Illinois
  • Sam Selmani, McGill University
  • Yan Soibelman, Kansas State University
  • Alan Thompson, Fields Institute
  • Michel van Garrell, Fields Institute
  • Johannes Walcher, McGill University
  • Noriko Yui, Queens University
  • Yuecheng Zhu, University of Texas at Austin

Monday, October 21st

Time

Event

Location

9:30-10:00am

Registration

Reception

10:00-10:10am

Jaume Gomis, Perimeter Institute
Welcome and Opening Remarks

Space Room

10:10-11:10am

Shamit Kachru, Stanford University
Some simple extensions of Mathieu Moonshine

Space Room

11:10-12:10pm

Ilarion Melnikov, Albert Einstein Institute
Hybrid conformal field theories

Space Room

12:10-2:30pm

Lunch

Bistro - 2nd Floor

2:30-3:30pm

Emanuel Diaconescu, Rutgers University
Coisotropic branes, surface defects and mirror symmetry

Space Room

 

Tuesday, October 22nd

Time

Event

Location

10:00-11:00am

Takuya Okuda, University of Tokyo
Exact results for boundaries and domain walls in
2d supersymmetric theories

Space Room

11:00-12:00pm

Kentaro Hori, Kavli IPMU
Exact Results In Two-Dimensional (2,2) Supersymmetric
Gauge Theories With Boundary

Space Room

12:00-2:30pm

Lunch

Bistro - 2nd Floor

2:30-3:30pm

Davide Gaiotto, Perimeter Institute
Algebraic structures in massive (2,2) theories

Space Room

3:30-3:45pm

Conference Photo

TBA

3:45-4:15pm 

Break

Bistro

4:15-5:15pm

Gaetan Borot, Max Planck Institute for Mathematics & MIT
Blobbed topological recursion

Space Room

 

Wednesday, October 23rd

Time

Event

Location

10:00-11:00am

Yan Soibelman, Kansas State University
Wall-crossing structures

Space Room

11:00-12:00pm

Albrecht Klemm, University of Bonn
On refined stable pair invariants for del Pezzo surfaces
and the 1/2 K3

Space Room

12:00-2:00pm

Lunch

Bistro - 2nd Floor

2:00-3:30pm

Marco Gualtieri, University of Toronto
Colloquium:  The Stokes groupoids

Theater

3:30-4:00pm

Break

Bistro

4:00-5:00pm

Marco Gualtieri, University of Toronto
A symplectic approach to generalized complex geometry

Space Room

6:00pm

Banquet

Bistro

 

Thursday, October 24th

Time

Event

Location

10:00-11:00am

Vincent Bouchard, University of Alberta
TBA

Space Room

11:00-12:00pm

Ricardo Couso, University of Santiago de Compostela
Resurgent transseries and the holomorphic anomaly

Space Room

12:00-2:30pm

Lunch

Bistro - 2nd Floor

2:30-3:30pm

David Favero, University of Alberta
TBA

Space Room

3:30-4:00pm

Break

Bistro

4:00-5:00pm

Callum Quigley, University of Alberta
Heterotic Flux Geometry from (0,2) Gauge Dynamics

Space Room

 

Friday, October 25th

Time

Event

Location

10:00-11:00am

Spiro Karigiannis, University of Waterloo
The mathematics of G_2 conifolds for M-theory

Space Room

11:00-12:00pm

Johannes Walcher, McGill University
TBA

Space Room

12:00-2:30pm

Lunch

Bistro - 2nd Floor

 

Gaetan Borot, Max Planck Institute for Mathematics & MIT

Blobbed topological recursion

Hermitian matrix models have been used since the early days of 2d quantum gravity, as generating series of discrete surfaces, and sometimes toy models for string theory. The single trace matrix models (with measure dM exp( - N Tr V(M)) have been solved in a 1/N expansion in the 90s by the moment method of Ambjorn et al. Later, Eynard showed that it can be rewritten more intrinsically in terms of algebraic geometry of the spectral curve, and formulated the so-called topological recursion.
In a similar way, we will show that double hermitian matrix models are solved by the same topological recursion, and more generally, that arbitrary hermitian matrix models are solved by a "blobbed topological recursion", whose properties still have to be investigated.
 
Ricardo Couso, University of Santiago de Compostela
 
Resurgent transseries and the holomorphic anomaly
 
Topological string theory is restricted enough to be solved completely in the perturbative sector, yet it is able to compute amplitudes in physical string theory and it also enjoys large N dualities. These gauge theory duals, sometimes in the form of matrix models, can be solved past perturbation theory by plugging transseries ansätze into the so called string equation. Based on the mathematics of resurgence, developed in the 80's by J. Ecalle, this approach has been recently applied with tremendous success to matrix models and their double scaling limits (Painlevé I, etc).  A natural question is if something similar can be done directly in the topological closed string sector. In this seminar I will show how the holomorphic anomaly equations of BCOV provide the starting point to derive a master equation which can be solved with a transseries ansatz. I will review the perturbative sector of the solutions, its structure, and how it generalizes for higher instanton nonperturbative sectors. Resurgence, in the guise of large order behavior of the perturbative sector, will be used to derive the holomorphicity of the instanton actions that control the asymptotics of the perturbative sector, and also to fix the holomorphic ambiguities in some cases. The example of local CP^2 will be used to illustrate these results.
This work is based on 1308.1695 and on-going research in collaboration with J.D. Edelstein, R. Schiappa and M. Vonk.
 
Davide Gaiotto, Perimeter Institute
 
Algebraic structures in massive (2,2) theories
 
I will review some ongoing work on the low energy properties of D-branes/boundary conditions in massive two-dimensional field theories with (2,2) supersymmetry. 
 
Marco Gualtieri, University of Toronto
 
A symplectic approach to generalized complex geometry
 
I will describe a new method for understanding a large class of generalized complex manifolds, in which we view them as usual symplectic structures on a manifold with a kind of log structure. I will explain this structure in detail and explain how it can be used to prove a Tian-Todorov unobstructedness theorem as well as topological
obstructions for existence of nondegenerate generalized complex structures.
 
Shamit Kachru, Stanford University
 
Some simple extensions of Mathieu Moonshine
 
Mathieu Moonshine is a striking and unexpected relationship between the sporadic simple finite group M24 and a special Jacobi form, the elliptic genus, which arises naturally in studies of nonlinear sigma models with K3 target.  In this talk, we first discuss its predecessor (Monstrous Moonshine), then discuss the current evidence in favor of Mathieu Moonshine.  We also discuss extensions of this story involving `second quantized mirror symmetry,' relating heterotic strings on K3 to type II strings on Calabi-Yau threefolds.
 
Ilarion Melnikov, Albert Einstein Institute
 
Hybrid conformal field theories
 
I will discuss a class of limiting points in the moduli space of d=2 (2,2) superconformal field theories.  These SCFTs arise as IR limits of "hybrid" UV theories constructed as a fibration of a Landau-Ginzburg theory over a base Kaehler geometry.  A significant generalization of Landau-Ginzburg and large radius geometric limit points, the hybrid theories can be used to probe general features of (2,2) and (0,2) SCFT moduli spaces. 
 
Takuya Okuda, University of Tokyo
 
Exact results for boundaries and domain walls in 2d supersymmetric theories
 
We apply supersymmetric localization to N=(2,2) gauged linear sigma models on a hemisphere, with boundary conditions, i.e., D-branes, preserving B-type supersymmetries. We explain how to compute the hemisphere partition function for each object in the derived category of equivariant coherent sheaves, and argue that it depends only on its K theory class. The hemisphere partition function computes exactly the central charge of the D-brane, completing the well-known formula obtained by an anomaly inflow argument. We also formulate supersymmetric domain walls as D-branes in the product of two theories.  We exhibit domain walls that realize the sl(2) affine Hecke algebra.  Based on arXiv:1308.2217.
 
Callum Quigley, University of Alberta
Heterotic Flux Geometry from (0,2) Gauge Dynamics
 
Chiral gauge theories in two dimensions with (0,2) supersymmetry admit a much broader, and more interesting, class of vacuum solutions than their better studied (2,2) counterparts. In this talk, we will explore some of the possibilities that are offered by this additional freedom by including field-dependent theta-angles and FI parameters. The moduli spaces that will result from this procedure correspond to heterotic string backgrounds with non-trivial H-flux and NS-brane sources. Along the way, a remarkable relationship between (0,2) gauge anomalies and H-flux will emerge.
 
Yan Soibelman, Kansas State University
 
Wall-crossing structures
 
The concept of wall-crossing structure (WCS for short) was introduced recently in my joint work with Maxim Kontsevich. WCS appear in different disguises in the theory of Donaldson-Thomas invariants of Calabi-Yau 3-folds, quiver representations,integrable systems of Hitchin type, cluster algebras, Mirror Symmetry, etc.
I plan to discuss the definition of WCS and illustrate it in several well-known examples. If time permits I will speak about a special class of WCS called rational WCS. It gives rise to wall-crossing formulas with factors which are algebraic functions. Conjecturally such WCS appear in Hitchin integrable systems with singularities.
 
Albrecht Klemm, University of Bonn
 
On refined stable pair invariants for del Pezzo surfaces and the 1/2 K3
 
TBA
 
Kentaro Hori, Klavi IPMU

Exact Results In Two-Dimensional (2,2) Supersymmetric Gauge Theories With Boundary

We compute the partition function on the hemisphere of a class of two-dimensional (2,2) supersymmetric field theories including gauged linear sigma models. The result provides a general exact formula for the central charge of the D-brane placed at the boundary. It takes the form of Mellin-Barnes integral and the question of its convergence leads to the grade restriction rule concerning branes near the phase boundaries. We find expressions in various phases including the large volume formula in which a characteristic class called the Gamma class shows up. The two sphere partition function factorizes into two hemispheres glued by inverse to the annulus. The result can also be written in a form familiar in mirror symmetry, and suggests a way to find explicit mirror correspondence between branes.

Spiro Karigiannis, University of Waterloo

The mathematics of G_2 conifolds for M-theory

G_2 manifolds play the analogous role in M-theory that Calabi-Yau manifolds play in string theory. There has been work in the physics community on conjectural "mirror symmetry" in this context, and it has also been observed that singularities are necessary for a satisfactory theory. After a very brief review of these physical developments (by a mathematician who doesn't necessarily understand the physics), I will give a mathematical introduction to G_2 conifolds. I will then proceed to give a detailed survey of recent mathematical developments on G_2 conifolds, including desingularization, deformation theory, and possible constructions of G_2 conifolds. This includes separate joint works of myself with Jason Lotay and with Dominic Joyce.

 

 
 
 
 

 

Vendredi oct 25, 2013
Speaker(s): 

 

Vendredi oct 25, 2013
Speaker(s): 

G_2 manifolds play
the analogous role in M-theory that Calabi-Yau manifolds play in string
theory. There has been work in the physics community on conjectural
"mirror symmetry" in this context, and it has also been observed that
singularities are necessary for a satisfactory theory. After a very
brief review of these physical developments (by a mathematician who
doesn't necessarily understand the physics), I will give a mathematical
introduction to G_2 conifolds. I will then proceed to give a detailed

Collection/Series: 

 

Jeudi oct 24, 2013
Speaker(s): 

Chiral gauge theories in two dimensions with (0,2) supersymmetry admit a
much broader, and more interesting, class of vacuum solutions than
their better studied (2,2) counterparts. In this talk, we will explore
some of the possibilities that are offered by this additional freedom by
including field-dependent theta-angles and FI parameters. The moduli
spaces that will result from this procedure correspond to heterotic
string backgrounds with non-trivial H-flux and NS-brane sources. Along

Collection/Series: 

 

Jeudi oct 24, 2013
Speaker(s): 

 

Jeudi oct 24, 2013
Speaker(s): 

Topological string theory is restricted enough to be solved
completely in the perturbative sector, yet it is able to compute
amplitudes in physical string theory and it also enjoys large N
dualities. These gauge theory duals, sometimes in the form of matrix
models, can be solved past perturbation theory by plugging transseries
ansätze into the so called string equation. Based on the mathematics of
resurgence, developed in the 80's by J. Ecalle, this approach has been

Collection/Series: 

 

Jeudi oct 24, 2013
Speaker(s): 

 

Mercredi oct 23, 2013
Speaker(s): 

I
will describe a new method for understanding a large class of

generalized complex manifolds, in which we view them as usual

symplectic structures on a manifold with a kind of log structure. I

will explain this structure in detail and explain how it can be used

to prove a Tian-Todorov unobstructedness theorem as well as

topological obstructions for existence of nondegenerate generalized

complex structures.

Collection/Series: 

 

Mercredi oct 23, 2013
Speaker(s): 

The concept of wall-crossing structure (WCS for short) was introduced
recently in my joint work with Maxim Kontsevich. WCS appear in different
disguises in the theory of Donaldson-Thomas invariants of Calabi-Yau
3-folds, quiver representations,integrable systems of Hitchin type,
cluster algebras, Mirror Symmetry, etc.
I plan to discuss the
definition of WCS and illustrate it in several well-known examples. If
time permits I will speak about a special class of WCS called rational

Collection/Series: 

 

Mardi oct 22, 2013
Speaker(s): 

Hermitian matrix models have been used since the early days of 2d
quantum gravity, as generating series of discrete surfaces, and
sometimes toy models for string theory. The single trace matrix models
(with measure dM exp( - N Tr V(M)) have been solved in a 1/N expansion
in the 90s by the moment method of Ambjorn et al. Later, Eynard showed
that it can be rewritten more intrinsically in terms of algebraic
geometry of the spectral curve, and formulated the so-called topological
recursion.

Collection/Series: 

Pages

Scientific Organizers

Vincent Bouchard, University of Alberta
Jaume Gomis, Perimeter Institute
Sergei Gukov, University of California, Santa Barbara
Johannes Walcher, McGill University
Shing-Tung Yau, Harvard University