Video Library

Since 2002 Perimeter Institute has been recording seminars, conference talks, and public outreach events using video cameras installed in our lecture theatres.  Perimeter now has 7 formal presentation spaces for its many scientific conferences, seminars, workshops and educational outreach activities, all with advanced audio-visual technical capabilities.  Recordings of events in these areas are all available On-Demand from this Video Library and on Perimeter Institute Recorded Seminar Archive (PIRSA)PIRSA is a permanent, free, searchable, and citable archive of recorded seminars from relevant bodies in physics. This resource has been partially modelled after Cornell University's arXiv.org. 

  

 

Sunday May 10, 2009
Speaker(s): 

The classical "split" rational R-matrix Poisson bracket structure on the space of rational connections over the Riemann sphere provides a natural setting for studying deformations. It can be shown that a natural set of Poisson commuting spectral invariant Hamiltonians, which are dual to the Casimir invariants of the Poisson structure, generate all deformations which, when viewed as nonautonomous Hamiltonian systems, preserve the generalized monodromy of the connections, in the sense of Birkhoff (i.e., the monodromy representation, the Stokes parameters and connection matrices).

 

Saturday May 09, 2009
Speaker(s): 

I will discuss the metric behavior of the Kahler-Ricci flow on Hirzebruch surfaces assuming that the initial metric is invariant under a maximal compact subgroup of the automorphism group. I will describe how, in the sense of Gromov-Hausdorff, the flow either shrinks to a point, collapses to P^1 or contracts an exceptional divisor. This confirms a conjecture of Feldman-Ilmanen-Knopf. This is a joint work with Jian Song.

 

Saturday May 09, 2009
Speaker(s): 

"In this joint work with Jingyi Chen and Weiyong He, we prove
existence of longtime smooth solutions to mean curvature flow of entire
Lipschitz Lagrangian graphs. A Bernstein type result for translating
solitons is also obtained."

 

Saturday May 09, 2009
Speaker(s): 

I will describe some combinatorial problems which arise when computing various types of partition functions for the Donaldson-Thomas theory of a space with a torus action. The problems are all variants of the following: give a generating function which enumerates the number of ways to pile n cubical boxes in the corner of a room. Often the resulting generating functions are nice product formulae, as predicted by the recent wall-crossing formulae of Kontsevich-Soibelman. There are now a variety of techniques, both geometric and combinatorial, to compute these formula.

 

Saturday May 09, 2009
Speaker(s): 

Inspired by homological mirror symmetry, Seidel and Thomas constructed braid group actions on derived categories of coherent sheaves of various varieties and proved faithfulness of such actions for braid groups of type A. I will discuss joint work with Hugh Thomas giving some faithfulness results for derived braid group actions of types D and E

 

Saturday May 09, 2009
Speaker(s): 

Quite a bit of progress has been achieved over the past seven years in understanding from a rigorous mathematical perspective the long time dynamics of waves in the Kerr geometry of a rotating black hole in equilibrium. A proof of the Penrose process for scalar waves has notably been given in this context. I will review some of these results, obtained in collaboration with Felix Finster, Joel Smoller and Shing-Tung Yau. I will also indicate a number of open problems.

 

Saturday May 09, 2009
Speaker(s): 

We produce new examples of Ricci solitons, including many of non-Kahler type, by looking for solutions with symmetries, thus reducing
the equations to dynamical systems

 

Saturday May 09, 2009
Speaker(s): 

"Sasakian geometry is often described as an odd dimensional counterparts of K\""ahler geometry. There is a natural Riemannian metric on the space of Sasakian metrics, which in turn gives a geodesic equation on this space. It can be viewed as parallel case of a well-known geodesic equation for the space of K\""ahler metrics. The equation is connected to some interesting geometric properties of Sasakian manifolds. It is a complicated complex Monge-Amp\`ere type involving

 

Friday May 08, 2009
Speaker(s): 

I'll discuss how to get an interesting invariant of submanifolds by using the ideas of string topology.

 

Friday May 08, 2009
Speaker(s): 

I will discuss the existence problem of extremal Kahler metrics (in the sense of Calabi) on the total space of a holomorphic projective bundle P(E) over a compact complex curve. The problem is not solved in full generality even in the case of a projective plane bundle over CP^1. However, I will show that sufficiently ``small'' Kahler classes admit extremal Kahler metrics if and only if the underlying vector bundle E can be decomposed as a sum of stable factors.

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