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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.
TBA
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
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
TBA
Resurgent transseries and the holomorphic anomaly
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
TBA
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.
On refined stable pair invariants for del Pezzo surfaces and the 1/2 K3
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
Blobbed topological recursion
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.
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