Since 2002 Perimeter Institute has been recording seminars, conference talks, public outreach events such as talks from top scientists 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 and 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.
Accessibly by anyone with internet, Perimeter aims to share the power and wonder of science with this free library.
The Conformal Method (as well as the closely related Conformal Thin Sandwich Method) has proven to be a very useful procedure both for constructing and for parametrizing solutions of the Einstein initial data constraint equations, for initial data sets with constant mean curvature (CMC). Is this true for non CMC data sets as well? After reviewing the CMC results, we discuss what we know and don't know about non CMC initial data sets and the effectiveness of the Conformal Method in handling them.
Evidence from several approaches to quantum gravity hints at the possibility that spacetime undergoes a "spontaneous dimensional reduction" at very short distances. If this is the case, the small scale universe might be described by a theory with two-dimensional conformal symmetry. I will summarize the evidence for dimensional reduction and indicate a tentative path towards using this conformal invariance to explore quantum gravity.
In 2-dim it is known that a unitary, well defined quantum field theory, if scale invariant must also be invariant under conformal transformations. Whether this is also true in dimensions higher than two has been an open question for decades. We have discovered renomalization group flows in 4-epsilon dimensions corresponding to scale but not conformal invariant theories. The flows correspond to limit cycles or ergodic behavior, neither of which had been reported in relativistic quantum field theories either.
TBA
I shall describe Relationalism, especially in the Leibniz-Mach-Barbour sense of the word and my variations on that theme. My presentation shall give five extensions to Barbour's work: (more or less) phase space, categorization, subsystems analysis, quantization, and physics as a propositional logic (`questions about physical systems'). I shall also briefly explain how some of Crane and Rovelli's ideas do fit within this scheme, whilst others are at odds with the LMB scheme, leaving one choosing options rather thanjust considering unions.
I will start by showing that gravity, with positive cosmological constant in 2+1 dimensions, can be formulated as a theory of dynamic conformal spatial geometry. Exploiting the isomorphism between the isometry group of de Sitter space in D+1 dimensions and the conformal group in D dimensions, I will reinterpret the Chern--Simons formulation of 2+1 gravity as a gauge theory of a conformal connection. In Cartan's generalization of geometry, this connection represents an evolving spatial geometry locally modeled off the conformal sphere.
I review the best-matching construction, and the striking properties of a Jacobi-type action first introduced by Baierelein, Sharp and Wheeler. The simplest theories compatible with such an action principle must have a universal light-cone and gauge symmetry. I also describe the implementation of three-dimensional conformal symmetries on the basis of the BSW action, which gives a first-principles derivation of York's solution of the initial value problem in General Relativity.
Shape Dynamics first arose as a theory of particle interactions formulated without any of Newton's absolute structures. Its fundamental arena is shape space, which is obtained by quotienting Newton's kinematic framework with respect to translations, rotations and dilatations. This leads to a universe defined purely intrinsically in relational terms. It is then postulated that a dynamical history is determined by the specification in shape space of an initial shape and an associated rate of change of shape. There is a very natural way to create a theory that meets such a requirement.
Check back for details on the next lecture in Perimeter's Public Lectures Series