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.
Although inflation is, by far, the best known mechanism to explain the observed properties of our Universe, there is still some room for alternative models, most of which implying a contracting phase preceding the current expanding one. Both phases are connected by a bounce at which the expansion rate must vanish. General relativity can only produce such a phase provided the spatial curvature is positive, in contradiction with the current observations.
In this talk, I will show that the five-dimensional Maxwell theory with a Chern-Simons coupling larger than a critical value in the Reissner-Nordstrom black hole geometry has tachyonic modes. This instability has an interesting property that it happens only at non-vanishing momenta, suggesting a spatially modulated phase transition in the holographically dual field theory. The final state after the phase transition has taken place will be discussed in detail in a special limit
We show that the generating function of the equivariant (generalized) Donaldson invariants of ${\bf R}^2 X {\Sigma}$ is captured by the solution of a thermodynamic Bethe ansatz equation. Based on a joint work with S. Shatashvili.
I will discuss a hybrid between Chern-Simons and Rozansky-Witten models. In particular, Wilson loops in this topological field theory are objects of a quantum deformation of the equivariant derived category of coherent sheaves.
I'll give an introduction to twistor-string theory, which is an attempt to reformulate supersymmetric gauge theory in four-dimensional space-time in terms of a certain generalisation of Gromov-Witten theory in twistor space. The resulting theory is closely related to the multi-dimensional residue calculus in G(k,n) (introduced in Cachazo's talk).
In the past year, motivated by physics, a rich structure has emerged from studying certain contour integrals in Grassmannians. Physical considerations single out a natural meromorphic form in G(k,n) with a cyclic structure. The residues obtained from these contour integrals have been shown to be invariants of a Yangian algebra. These residues also control what happens deep inside collisions of protons taking place at colliders like the Large Hadron Collider or LHC at CERN.
I will give an overview of recent work with Davide Gaiotto and Greg Moore. This work relates the phenomenon of ''wall-crossing'' for BPS states in four-dimensional N=2 theories to a new construction of hyperkahler metrics. These metrics include in particular the metrics on moduli spaces of solutions to Hitchin equations. I will also briefly describe some extensions of this work to incorporate line and surface operators in the N=2 theory (in progress).
The study of D-branes at singular points of Calabi-Yau threefolds has revealed interesting connections between certain noncommutative algebras and singular algebraic varieties. In many respects, the choice of an appropriate noncommutative algebra is analogous to finding a resolution of singularities of the variety. We will explain this connection in detail, and outline a program for studying such ''noncommutative resolutions'' globally, for compact algebraic (Calabi--Yau) threefolds.
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, and reducible. However if X is a smooth Calabi-Yau threefold, X[n] has a canonical virtual motive --- a motification of the degree zero Donaldson-Thomas invariants. We give a formula analogous to Gottsche's for the virtual motive of X[n].