Format results
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A black hole uniqueness theorem
Spyros Alexakis - University of Toronto
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Algebraically special solutions in higher dimensions
Harvey Reall - University of Cambridge
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Lattice points in moduli spaces of curves
Norman Do - McGill University
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Topological recursion and mirror symmetry
Vincent Bouchard - University of Alberta
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On the notion quasilocal mass in general relativity
Mu-Tao Wang - Columbia University
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Heterotic string and complex Monge-Ampere equation
Shing-Tung Yau - Harvard University
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Topological defects in gauge theories.
Magdalena Czubak - University of Colorado Boulder
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Representations of Generalized Clifford Algebras
Emre Coskun - Western University
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Motivic degree zero Donaldson - Thomas invariants
Jim Bryan - University of British Columbia
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A black hole uniqueness theorem
Spyros Alexakis - University of Toronto
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… -
Algebraically special solutions in higher dimensions
Harvey Reall - University of Cambridge
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… -
Lattice points in moduli spaces of curves
Norman Do - McGill University
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… -
Categorical Lie algebra actions and braid group actions
We will discuss the notion of categorical Lie algebra actions, as introduced by Rouquier and Khovanov-Lauda. 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… -
Topological recursion and mirror symmetry
Vincent Bouchard - University of Alberta
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… -
Normal Forms for Lattice Polarized K3 Surfaces and the Kuga-Satake Hodge Conjecture
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 two-isogeny relates these K3 surfaces to the Kummer K3 surfaces of principally polarized abelian surfaces, with the… -
On the notion quasilocal mass in general relativity
Mu-Tao Wang - Columbia University
There have been many attempts to define quasilocal mass for a spacelike 2-surface in a spacetime by the Hamilton-Jacobi 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… -
Heterotic string and complex Monge-Ampere equation
Shing-Tung Yau - Harvard University
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. -
Topological defects in gauge theories.
Magdalena Czubak - University of Colorado Boulder
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. -
Representations of Generalized Clifford Algebras
Emre Coskun - Western University
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… -
Motivic degree zero Donaldson - Thomas invariants
Jim Bryan - University of British Columbia
The Hilbert scheme X[n] of n points on variety X parameterizes length n, zero dimensional subschemes of X. When X is a smooth surface, X[n] is also smooth and a beautiful formula for its motive was determined by Gottsche. When X is a threefold, X[n] is in general singular, of the wrong dimension… -
The coherent-constructible correspondence and homological mirror symmetry for toric varieties
Chiu-Chu Liu - Columbia University
The Hilbert scheme X[n] of n points on variety X parameterizes length n, zero dimensional subschemes of X. When X is a smooth surface, X[n] is also smooth and a beautiful formula for its motive was determined by Gottsche. When X is a threefold, X[n] is in general singular, of the wrong dimension…