This series covers all areas of research at Perimeter Institute, as well as those outside of PI's scope.
Current progress in quantum field theory is largely driven by the conformal bootstrap program, which aims to classify the space and properties of conformal field theories using symmetries and other fundamental constraints. In the context of the AdS/CFT Correspondence, this increasingly sophisticated endeavor doubles as a probe of foundations of quantum gravity.
3d quantum gravity is a beautiful toy-model for 4d quantum gravity: it is much simpler, it does not have local degrees of freedom, yet retains enough complexity and subtlety to provide a non-trivial example of dynamical quantum geometry and open new directions of research in physics and mathematics. I will present the Ponzano-Regge model, introduced in 1968, built from tetrahedra “quantized" as 6j-symbols from the theory of recoupling of spins.
Strong gravitational lenses with measured time delays between the multiple images can be used to determine the Hubble-Lemaitre constant (H0) that sets the expansion rate of the Universe. An independent determination of H0 is important to ascertain the possible need of new physics beyond the standard cosmological model, given the tension in current H0 measurements. A program initiated to measure H0 to <3.5% in precision from strongly lensed quasars is in progress, and I will present the latest results and their implications. Search is underway to find new lenses in imaging surveys.
The discovery of a Higgs like boson at LHC in 2012 was a development of fundamental importance in particle physics.
Applications of physics to geometry have deep historical roots going back at least to Archimedes, while recent decades have seen structures of classical and quantum gauge theory lead to enormous advances in the theory of three and four manifolds. Meanwhile, geometry provides conceptual tools for physics as foundational as variational principles, the kinematics of spacetime, and the topological classification of matter. This talk will describe some possibilities for bringing number theory, more specifically, *arithmetic geometry* into this interaction.
Many of the rich interactions between mathematics and physics arise using general mathematical frameworks that describe a host of physical phenomena: from differential equations, to algebra, to topology and geometry. On the other hand, mathematics also possesses many examples of "exceptional objects": they constitute the finite set of leftovers that appear in numerous classification problems.
The cosmic microwave background radiation has been an indispensable tool for learning about the origins and evolution of our Observable Universe. Satellites and ground based experiments measuring the temperature and polarization anisotropies with ever increasing angular resolution and sensitivity have established the standard cosmological model, LCDM, and constrained or ruled out a huge variety of theoretical models of the early Universe.
Sexual harassment and sexual assault in the workplace is almost always a severe betrayal of trust. I will describe research and theory that my students and I have developed over the last 25 years regarding interpersonal and institutional betrayals of trust. My presentation will include an explanation of betrayal trauma theory and information about institutional betrayal. I will present data from some of our research studies, including results from a study of sexual harassment of graduate students. Included will be research-based recommendations for how to respond well to disclosures o
From earliest infancy, we live in and learn to function in a world of causes and effects. Yet science has had an ambivalent, even hostile attitude toward causation for more than a century. Statistics courses teach us that “correlation is not causation,” yet they are strangely silent about what is causation.
While it’s undeniably sexy to work with infinite-dimensional categories “model-independently,” we contend there is a categorical imperative to familiarize oneself with at least one concrete model in order to check that proposed model-independent constructions interpret correctly. With this aim in mind, we recount the n-complicial sets model of (∞,n)-categories for 0 ≤ n ≤ ∞, the combinatorics of which are quite similar to its low-dimensional special cases: quasi-categories (n=1) and Kan complexes (n=0).