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.
I will discuss some results on double loop groups that point to geometric phenomena about double affine flag varieties and double affine Grassmannian. One result of this study is a definition of double affine Kazhdan-Lusztig polynomials.
It is commonly believed that quantum information is not lost in a black hole. Instead, it is encoded into non-local degrees of freedom in some clever way; like a quantum error-correcting code. In this talk, I will discuss how one may resolve some paradoxes in quantum gravity by using the theory of quantum error-correction. First, I will introduce a simple toy model of the AdS/CFT correspondence based on tensor networks and demonstrate that the correspondence between the AdS gravity and CFT is indeed a realization of quantum codes.
For a family of finite rate stabilizer codes, one can define two distinct error correction thresholds: the usual "block" threshold for the entire code, and the single-qubit threshold, where we only care about the stability of a single encoded qubit corresponding to a randomly chosen conjugate pair of logical X and Z operators. Our main result is that in the case of erasures, for hyperbolic surface codes related to a {p,q} tiling of the hyperbolic plane, it is the latter threshold that coincides exactly with the infinite-graph edge percolation transition. I will also
General relativity taught us that space time is dynamical and quantum theory posits that dynamical objects are quantum. Hence the Newtonian notion of space time as a passive stage where physics takes place needs to be replaced by a notion of quantum space time which is interacting with all other quantum matter fields.
I discuss a string theoretic approach to integrable lattice models. This approach provides a unified perspective on various important notions in lattice models, and relates these notions to four-dimensional N = 1 supersymmetric field theories and their surface operators. I explain how my construction connects to Costello's work and the Nekrasov-Shatashvili correspondence.
The properties of physical processes reflect themselves in the structure of the relevant observables. This idea has been largely exploited for the flat space S-matrix, whose analytic structure is determined by locality and unitary, the two pillars which our current understanding of nature is based on. In this context, it has been possible to find new mathematical structures whose properties turn out to be the ones we ascribe to scattering processes in flat-space, so that both unitarity and locality can be viewed as emergent from some more fundamental structure.