Connections in Geometry and Physics 2010
Organizer(s): Robert Myers Spiro Karigiannis Ruxandra Moraru Marco Gualtieri McKenzie Wang
Collection URL: http://pirsa.org/C10011
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A black hole uniqueness theorem Speaker(s): Spyros Alexakis
Abstract: I will discuss recent joint work with A. Ionescu and S. Klainerman on the black hole uniqueness problem. A classical result of Hawking (building on earlier work of Carter and Robinson) asserts that any vacuum, stationary black hole exterior region must be isometric to the Kerr exterior, under the re... read more
Date: 07/05/2010  8:30 am
Collection: Connections in Geometry and Physics 2010

Algebraically special solutions in higher dimensions Speaker(s): Harvey Reall
Abstract: The Petrov classification of the Weyl tensor is an important tool in the study of exact solutions of the Einstein equation in 4d. For example, the Kerr solution was discovered in a study of spacetimes with algebraically special Weyl tensors. Algebraic classification of the Weyl tensor has been exten... read more
Date: 07/05/2010  10:00 am
Collection: Connections in Geometry and Physics 2010

Lattice points in moduli spaces of curves Speaker(s): Norman Do
Abstract: There appear to be only two essentially distinct ways to understand intersection numbers on moduli spaces of curves  via Hurwitz numbers or symplectic volumes. In this talk, we will consider polynomials defined by Norbury which bridge the gap between these two pictures. They appear in the enumera... read more
Date: 07/05/2010  11:15 am
Collection: Connections in Geometry and Physics 2010

Categorical Lie algebra actions and braid group actions Speaker(s): Joel Kamnitzer
Abstract: We will discuss the notion of categorical Lie algebra actions, as introduced by Rouquier and KhovanovLauda. In particular, we will give examples of categorical Lie algebra actions on derived categories of coherent sheaves. We will show that such categorical Lie algebra actions lead to actions of br... read more
Date: 07/05/2010  1:45 pm
Collection: Connections in Geometry and Physics 2010

Topological recursion and mirror symmetry Speaker(s): Vincent Bouchard
Abstract: The topological recursion of Eynard and Orantin has found many applications in various areas of mathematics. In this talk I will discuss the recursion from the point of view of Hurwitz numbers and local mirror symmetry. I will explain the mathematics underlying the recursion, its relation with the c... read more
Date: 07/05/2010  3:15 pm
Collection: Connections in Geometry and Physics 2010

Normal Forms for Lattice Polarized K3 Surfaces and the KugaSatake Hodge Conjecture Speaker(s): Charles Doran
Abstract: We introduce a projective hypersurface ''normal form'' for a class of K3 surfaces which generalizes the classical Weierstrass normal form for complex elliptic curves. A geometric twoisogeny relates these K3 surfaces to the Kummer K3 surfaces of principally polarized abelian surfaces, with the norma... read more
Date: 07/05/2010  4:30 pm
Collection: Connections in Geometry and Physics 2010

On the notion quasilocal mass in general relativity Speaker(s): MuTao Wang
Abstract: There have been many attempts to define quasilocal mass for a spacelike 2surface in a spacetime by the HamiltonJacobi method. The essential difficulty in this approach is the choice of the background configuration to be subtracted from the physical Hamiltonian. The quasilocal mass should be positi... read more
Date: 08/05/2010  8:30 am
Collection: Connections in Geometry and Physics 2010

Heterotic string and complex MongeAmpere equation Speaker(s): ShingTung Yau
Abstract: I will talk about the work that I did with Jixiang Fu and Jun Li on the Strominger system and their role in string theory.
Date: 08/05/2010  10:00 am
Collection: Connections in Geometry and Physics 2010

Topological defects in gauge theories. Speaker(s): Magdalena Czubak
Abstract: We discuss recent progress on the rigorous description of the dynamics of the energy concentration sets in the abelian Higgs model. This is joint work with R. Jerrard.
Date: 08/05/2010  11:15 am
Collection: Connections in Geometry and Physics 2010

Representations of Generalized Clifford Algebras Speaker(s): Emre Coskun
Abstract: Clifford algebras arose in Dirac's work on the relativistic wave equation in quantum mechanics. Using the Clifford algebra associated to a quadratic form on a finite dimensional vector space, one can reduce the relativistic wave equation, a PDE of order two, to a system of linear PDEs. Similarly, on... read more
Date: 08/05/2010  1:00 pm
Collection: Connections in Geometry and Physics 2010

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