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Resurgent transseries and the holomorphic anomaly

October 24, 2013

PIRSA:13100123
13/14 PSI - Statistical Mechanics - Lecture 13

Anton Burkov University of Waterloo

October 24, 2013

PIRSA:13100061
TBA

Vincent Bouchard University of Alberta

October 24, 2013

PIRSA:13100122
A symplectic approach to generalized complex geometry

Marco Gualtieri University of Toronto

October 23, 2013

PIRSA:13100121
13/14 PSI - Quantum Field Theory I - Lecture 11

Freddy Cachazo Perimeter Institute for Theoretical Physics

October 23, 2013

PIRSA:13100036
The Stokes groupoids

Marco Gualtieri University of Toronto

October 23, 2013

PIRSA:13100110
On refined stable pair invariants for del Pezzo surfaces and the 1/2 K3

Albrecht Klemm Rheinische Friedrich-Wilhelms-Universität Bonn

October 23, 2013

PIRSA:13100120
13/14 PSI - Statistical Mechanics - Lecture 12

Anton Burkov University of Waterloo

October 23, 2013

PIRSA:13100060
Topics in QFT on Flat and Curved Spacetimes - Lecture 10

Ugo Moschella University of Insubria

October 23, 2013

PIRSA:13100018
Wall-crossing structures

Yan Soibelman Kansas State University

October 23, 2013

PIRSA:13100119
Blobbed topological recursion

Gaetan Borot

October 22, 2013

PIRSA:13100118
General Relativity for Cosmology - Lecture 11

Achim Kempf University of Waterloo

October 22, 2013

PIRSA:13100004

Resurgent transseries and the holomorphic anomaly

October 24, 2013

PIRSA:13100123

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.
13/14 PSI - Statistical Mechanics - Lecture 13

Anton Burkov University of Waterloo

October 24, 2013

PIRSA:13100061
TBA

Vincent Bouchard University of Alberta

October 24, 2013

PIRSA:13100122
A symplectic approach to generalized complex geometry

Marco Gualtieri University of Toronto

October 23, 2013

PIRSA:13100121

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.
13/14 PSI - Quantum Field Theory I - Lecture 11

Freddy Cachazo Perimeter Institute for Theoretical Physics

October 23, 2013

PIRSA:13100036
The Stokes groupoids

Marco Gualtieri University of Toronto

October 23, 2013

PIRSA:13100110

Ordinary differential equations become much less ordinary when they are allowed to have singularities. Solving them naively in formal power series, one often obtains divergent series, just as in the perturbation series for physical observables in quantum field theory. The asymptotic interpretation of this divergent series exhibits the famous Stokes phenomenon, an essential ingredient in any full description of the solutions to the system. I will explain a new viewpoint on singular ODE which illuminates the geometric meaning of the phenomena described above, and which can be applied to the problem of resummation of formal power series. This viewpoint uses a very basic but underused tool in differential geometry: Lie groupoids. A Lie groupoid is as natural and essential an object as a Lie group; I shall explain how to build examples of them and how to use them to solve singular differential equations.
On refined stable pair invariants for del Pezzo surfaces and the 1/2 K3

Albrecht Klemm Rheinische Friedrich-Wilhelms-Universität Bonn

October 23, 2013

PIRSA:13100120
13/14 PSI - Statistical Mechanics - Lecture 12

Anton Burkov University of Waterloo

October 23, 2013

PIRSA:13100060
Topics in QFT on Flat and Curved Spacetimes - Lecture 10

Ugo Moschella University of Insubria

October 23, 2013

PIRSA:13100018
Wall-crossing structures

Yan Soibelman Kansas State University

October 23, 2013

PIRSA:13100119

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.
Blobbed topological recursion

Gaetan Borot

October 22, 2013

PIRSA:13100118

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.
General Relativity for Cosmology - Lecture 11

Achim Kempf University of Waterloo

October 22, 2013

PIRSA:13100004

Title	Date	Collection	Type	Info
Resurgent transseries and the holomorphic anomaly	2013‑10‑24	Physics Around Mirror Symmetry	Conference	View details
13/14 PSI - Statistical Mechanics - Lecture 13	2013‑10‑24	13/14 PSI - Statistical Mechanics	Course	View details
TBA	2013‑10‑24	Physics Around Mirror Symmetry	Conference	View details
A symplectic approach to generalized complex geometry	2013‑10‑23	Physics Around Mirror Symmetry	Conference	View details
13/14 PSI - Quantum Field Theory I - Lecture 11	2013‑10‑23	13/14 PSI - Quantum Field Theory I	Course	View details
The Stokes groupoids	2013‑10‑23	Colloquium	Scientific Series	View details
On refined stable pair invariants for del Pezzo surfaces and the 1/2 K3	2013‑10‑23	Physics Around Mirror Symmetry	Conference	View details
13/14 PSI - Statistical Mechanics - Lecture 12	2013‑10‑23	13/14 PSI - Statistical Mechanics	Course	View details
Topics in QFT on Flat and Curved Spacetimes - Lecture 10	2013‑10‑23	Topics in QFT on Flat and Curved Spacetimes	Course	View details
Wall-crossing structures	2013‑10‑23	Physics Around Mirror Symmetry	Conference	View details
Blobbed topological recursion	2013‑10‑22	Physics Around Mirror Symmetry	Conference	View details
General Relativity for Cosmology - Lecture 11	2013‑10‑22	General Relativity for Cosmology - 2013	Course	View details

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