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.
In this talk (based on arXiv:1001.0354) we give a quantum statistical interpretation for the Kauffmann bracket polynomial state sum <K> for the Jones polynomial. We use this quantum mechanical interpretation to give a new quantum algorithm for computing the Jones polynomial. This algorithm is useful for its conceptual simplicity, and it applies to all values of the polynomial variable that lie on the unit circle in the complex plane.
Fibonacci anyons are the simplest system of anyons capable of implementing universal topological quantum computation, an area which is of intense theoretical and experimental interest. Recent studies have shown that for nearest-neighbour interactions, the properties of the ground state of a 1-D chain of Fibonacci anyons may be modeled using a spin chain, and are related to specific conformal field theories.
Theoretical insights originated from the study of black holes combined with developments in string theory indicate that space time and gravity are emergent. A central role in these developments is played by the holographic principle. I will present a heuristic argument that indicates that at a microscopic level gravity is an entropic force caused by changes in the available phase space due to the displacement of material bodies.
Two-dimensional non-linear sigma models on some supergroup manifolds
are conformal field theories whether the action includes a Wess-Zumino
term or not. These models are relevant for the worldsheet description
of string theory in Anti-de Sitter backgrounds with Ramond-Ramond
fluxes. The current algebra is an useful tool to study these theories.
In these lectures I will review the construction of the current
algebra. Then I will discuss some applications to the computation of
the spectrum and integrability.
We first discuss quantum measure and integration theory. We then consider various anhomomorphic logics. Finally, we present some connections between the two theories. One connection is transferring a quantum measure to a measure on an anhomomorphic logic. Another is the creation of a reality filter that is stronger than Sorkin's preclusivity. This is accomplished by generating a preclusive coevent from a quantum measure. No prior knowledge of quantum measure theory or anhomomorphic logics will be assumed.
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.