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The mathematics of G_2 conifolds for M-theory

Spiro Karigiannis University of Waterloo

October 25, 2013

PIRSA:13100126
General Relativity for Cosmology - Lecture 12

Achim Kempf University of Waterloo

October 24, 2013

PIRSA:13100009
Heterotic Flux Geometry from (0,2) Gauge Dynamics

Callum Quigley Kirkland & Ellis

October 24, 2013

PIRSA:13100125
13/14 PSI - Quantum Field Theory I - Lecture 12

Freddy Cachazo Perimeter Institute for Theoretical Physics

October 24, 2013

PIRSA:13100037
TBA

David Favero

October 24, 2013

PIRSA:13100124
Asymptotically safe matrix models

Tim Koslowski Technical University of Applied Sciences Würzburg-Schweinfurt
October 24, 2013

PIRSA:13100067
Quantum Gravity
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

The mathematics of G_2 conifolds for M-theory

Spiro Karigiannis University of Waterloo

October 25, 2013

PIRSA:13100126

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.
General Relativity for Cosmology - Lecture 12

Achim Kempf University of Waterloo

October 24, 2013

PIRSA:13100009
Heterotic Flux Geometry from (0,2) Gauge Dynamics

Callum Quigley Kirkland & Ellis

October 24, 2013

PIRSA:13100125

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.
13/14 PSI - Quantum Field Theory I - Lecture 12

Freddy Cachazo Perimeter Institute for Theoretical Physics

October 24, 2013

PIRSA:13100037
TBA

David Favero

October 24, 2013

PIRSA:13100124
Asymptotically safe matrix models

Tim Koslowski Technical University of Applied Sciences Würzburg-Schweinfurt
October 24, 2013

PIRSA:13100067
Quantum Gravity
The functional renormalization group is a tool in the systematic search for Euclidean QFTs that works with very little input: All one needs to specify is a field content, symmetries and a notion of locality. The functional renormalization group then allows one to scan this theory space for bare actions for which the path integral can be performed nonperturbatively. These actions appear as fixed points (and relevant deformations) of the renormalization group flow (so-called asymptotic safety). Such a systematic search has so far not been performed for the tensor model approach to quantum gravity. We investigate matrix models for 2-dimensional gravity and the Grosse-Wulkenhaar model, which is a simple tensor model for a 4D noncommutative scalar field theory, as a first step. I will report on work, done in collaboration with Astrid Eichhorn and Alessandro Sfondrini, where we confirmed asymptotic safety purely through functional RG methods. Based on the lessons learned from these models I will summarize how the usual continuum RG approach has to be generalized for the investigation of tensor models and conclude with a recipe for the investigation of general tensor models.
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.

Title	Date	Collection	Type	Info
The mathematics of G_2 conifolds for M-theory	2013‑10‑25	Physics Around Mirror Symmetry	Conference	View details
General Relativity for Cosmology - Lecture 12	2013‑10‑24	General Relativity for Cosmology - 2013	Course	View details
Heterotic Flux Geometry from (0,2) Gauge Dynamics	2013‑10‑24	Physics Around Mirror Symmetry	Conference	View details
13/14 PSI - Quantum Field Theory I - Lecture 12	2013‑10‑24	13/14 PSI - Quantum Field Theory I	Course	View details
TBA	2013‑10‑24	Physics Around Mirror Symmetry	Conference	View details
Asymptotically safe matrix models	2013‑10‑24	Quantum Gravity	Scientific Series	View details
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

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