C05002 - Generalized Geometries in String Theory Minicourse lectures by Marco Gualtieri, Yi Li and Mariana Granas. http://pirsa.org/podcast/C05002 Science 2012 http://blogs.law.harvard.edu/tech/rss en-ca Thu, 09 Feb 2012 04:32:52 -0500 sbradwell@perimeterinstitute.ca Thu, 09 Feb 2012 04:32:52 -0500 G 180 pirsa-admin@perimeterinstitute.ca Steve Bradwell's - Podcast Generator Generalized Geometric Structures (Part 1) Marco Gualtieri http://streamer.perimeterinstitute.ca/mp3/d4cffe32-f5be-44d3-9289-1b58ac0f4e7e.mp3 Science http://streamer.perimeterinstitute.ca/mp3/d4cffe32-f5be-44d3-9289-1b58ac0f4e7e.mp3 Tue, 15 Feb 2005 11:00:00 -0500 Twisted Generalized Calabi-Yau Manifolds and Topological Sigma Models with Flux (Part 1) In these lectures, we examine how twisted generalized Calabi-Yau (GCY) manifolds arise in the construction of a general class of topological sigma models with non-trivial three-form flux. The topological sigma model defined on a twisted GCY can be regarded as a simultaneous generalization of the more familiar A-model and B-model. Emphasis will be given to the relation between topological observables of the sigma model and a Lie algebroid cohomology intrinsically associated with the twisted GCY. If time permits, we shall also discuss topological D-branes in this more general setting, and explain how the viewpoint from the Lie algebroid helps to elucidate certain subtleties even for the conventional A-branes and B-branes. The lectures will be physically motivated, although I will try to make the presentation self-contained for both mathematicians and physicists. Yi Li http://streamer.perimeterinstitute.ca/mp3/9b52c19e-e06a-434f-b7b8-8a409beee77a.mp3 Science http://streamer.perimeterinstitute.ca/mp3/9b52c19e-e06a-434f-b7b8-8a409beee77a.mp3 Tue, 15 Feb 2005 14:00:00 -0500 Generalized Geometric Structures (Part 2) Marco Gualtieri http://streamer.perimeterinstitute.ca/mp3/0699e1fb-8699-4a40-b9ab-435b156a1d9b.mp3 Science http://streamer.perimeterinstitute.ca/mp3/0699e1fb-8699-4a40-b9ab-435b156a1d9b.mp3 Wed, 16 Feb 2005 11:00:00 -0500 Twisted Generalized Calabi-Yau Manifolds and Topological Sigma Models with Flux (Part 2) In these lectures, we examine how twisted generalized Calabi-Yau (GCY) manifolds arise in the construction of a general class of topological sigma models with non-trivial three-form flux. The topological sigma model defined on a twisted GCY can be regarded as a simultaneous generalization of the more familiar A-model and B-model. Emphasis will be given to the relation between topological observables of the sigma model and a Lie algebroid cohomology intrinsically associated with the twisted GCY. If time permits, we shall also discuss topological D-branes in this more general setting, and explain how the viewpoint from the Lie algebroid helps to elucidate certain subtleties even for the conventional A-branes and B-branes. The lectures will be physically motivated, although I will try to make the presentation self-contained for both mathematicians and physicists. Yi Li http://streamer.perimeterinstitute.ca/mp3/10ba6808-d3ef-43d4-a690-107c78750733.mp3 Science http://streamer.perimeterinstitute.ca/mp3/10ba6808-d3ef-43d4-a690-107c78750733.mp3 Wed, 16 Feb 2005 14:00:00 -0500 Generalized Geometric Structures (Part 3) Marco Gualtieri http://streamer.perimeterinstitute.ca/mp3/c2d6926d-c407-4e9c-92e6-7a61951604ed.mp3 Science http://streamer.perimeterinstitute.ca/mp3/c2d6926d-c407-4e9c-92e6-7a61951604ed.mp3 Thu, 17 Feb 2005 11:00:00 -0500 Twisted Generalized Calabi-Yau Manifolds and Topological Sigma Models with Flux (Part 3) In these lectures, we examine how twisted generalized Calabi-Yau (GCY) manifolds arise in the construction of a general class of topological sigma models with non-trivial three-form flux. The topological sigma model defined on a twisted GCY can be regarded as a simultaneous generalization of the more familiar A-model and B-model. Emphasis will be given to the relation between topological observables of the sigma model and a Lie algebroid cohomology intrinsically associated with the twisted GCY. If time permits, we shall also discuss topological D-branes in this more general setting, and explain how the viewpoint from the Lie algebroid helps to elucidate certain subtleties even for the conventional A-branes and B-branes. The lectures will be physically motivated, although I will try to make the presentation self-contained for both mathematicians and physicists. Yi Li http://streamer.perimeterinstitute.ca/mp3/6b76d6da-315a-456d-955d-297f6e40d9c1.mp3 Science http://streamer.perimeterinstitute.ca/mp3/6b76d6da-315a-456d-955d-297f6e40d9c1.mp3 Thu, 17 Feb 2005 14:00:00 -0500 Supergravity Backgrounds from Generalized Calabi-Yau Manifolds (Part 1) We will see how generalized Calabi-Yau manifolds as defined by Hitchin emerge from supersymmetry equations in type II theories. In the first lecture, we will review the formalism of G-structures, which is central in the context of compactification with fluxes. In the second lecture we will see how (twisted) generalized Calabi-Yau manifolds emerge from supersymmetry equations using SU(3) structure. In the last lecture, we will discuss special features about compactifications on Generalized Calabi-Yau's. Mariana Granas http://streamer.perimeterinstitute.ca/mp3/c17b7d1f-644d-42b5-beda-27f5d6b91977.mp3 Science http://streamer.perimeterinstitute.ca/mp3/c17b7d1f-644d-42b5-beda-27f5d6b91977.mp3 Tue, 01 Mar 2005 11:00:00 -0500 Supergravity Backgrounds from Generalized Calabi-Yau Manifolds (Part 2) Mariana Granas http://streamer.perimeterinstitute.ca/mp3/24bd24df-8722-4e12-a681-3b7b89f9df44.mp3 Science http://streamer.perimeterinstitute.ca/mp3/24bd24df-8722-4e12-a681-3b7b89f9df44.mp3 Wed, 02 Mar 2005 11:00:00 -0500