COVID-19 information for PI Residents and Visitors
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 |
Space Room |
10:10-11:10am |
Shamit Kachru, Stanford University |
Space Room |
11:10-12:10pm |
Ilarion Melnikov, Albert Einstein Institute |
Space Room |
12:10-2:30pm |
Lunch |
Bistro - 2nd Floor |
2:30-3:30pm |
Emanuel Diaconescu, Rutgers University |
Space Room |
Tuesday, October 22nd
Time |
Event |
Location |
10:00-11:00am |
Takuya Okuda, University of Tokyo |
Space Room |
11:00-12:00pm |
Kentaro Hori, Kavli IPMU |
Space Room |
12:00-2:30pm |
Lunch |
Bistro - 2nd Floor |
2:30-3:30pm |
Davide Gaiotto, Perimeter Institute |
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 |
Space Room |
Wednesday, October 23rd
Time |
Event |
Location |
10:00-11:00am |
Yan Soibelman, Kansas State University |
Space Room |
11:00-12:00pm |
Albrecht Klemm, University of Bonn |
Space Room |
12:00-2:00pm |
Lunch |
Bistro - 2nd Floor |
2:00-3:30pm |
Marco Gualtieri, University of Toronto |
Theater |
3:30-4:00pm |
Break |
Bistro |
4:00-5:00pm |
Marco Gualtieri, University of Toronto |
Space Room |
6:00pm |
Banquet |
Bistro |
Thursday, October 24th
Time |
Event |
Location |
10:00-11:00am |
Vincent Bouchard, University of Alberta |
Space Room |
11:00-12:00pm |
Ricardo Couso, University of Santiago de Compostela |
Space Room |
12:00-2:30pm |
Lunch |
Bistro - 2nd Floor |
2:30-3:30pm |
David Favero, University of Alberta |
Space Room |
3:30-4:00pm |
Break |
Bistro |
4:00-5:00pm |
Callum Quigley, University of Alberta |
Space Room |
Friday, October 25th
Time |
Event |
Location |
10:00-11:00am |
Spiro Karigiannis, University of Waterloo |
Space Room |
11:00-12:00pm |
Johannes Walcher, McGill University |
Space Room |
12:00-2:30pm |
Lunch |
Bistro - 2nd Floor |
Gaetan Borot, Max Planck Institute for Mathematics & MIT
Blobbed topological recursion
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.
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.
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.
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
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
Coisotropic branes, surface defects and mirror symmetry
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.
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.
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