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 I will give an overview of localization and some of its applications for QFTs in three dimensions. I will start by reviewing the localization procedure for N=2 supersymmetric gauge theories in three dimensions on S^3. I will then describe some of the applications to field theory dualities and to holography, and the possibility of extracting information about RG fixed points from the localized partition function.
It is my contention that non-commutative geometry is really "ordinary geometry" carried out in a non-commutative logic. I will sketch a specific project, relating groupoid C*-algebras to toposes, by means of which I hope to detect the nature of this non-commutative logic.
I briefly introduce the recently introduced idea of relativity of locality, which is a
consequence of a non-flat geometry of momentum space. Momentum space
can acquire nontrivial geometrical properties due to quantum gravity effects.
I study the relation of this framework with noncommutative geometry, and the
Quantum Group approach to noncommutative spaces. In particular I'm interested
in kappa-Poincaré, which is a Quantum Group that, as shown by Freidel and Livine,
in the 1+1D case emerges as the symmetry of effective field theory coupled with