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.
The mathematical notion of moonshine relates the theory of finite groups with that of modular objects. The first example, 'Monstrous Moonshine', was clarified in the context of two dimensional conformal field theory in the 90's. In 2010, interest in moonshine in the physics community was reinvigorated when Eguchi et. al. observed representations of the finite group M24 appearing in the elliptic genus of nonlinear sigma models on K3.
I will present a 'categorical' way of doing analytic geometry in which analytic geometry is seen as a precise analogue of algebraic geometry.
Our approach works for both complex analytic geometry and p-adic analytic geometry in a uniform way. I will focus on the idea of an 'open set' as used in various geometrical theories and how it is characterized
I will define coisotropic structures in the setting of shifted Poisson geometry in two ways and show their equivalence. The interplay between the definitions allows one to produce nontrivial statements. I will also describe some examples of coisotropic structures. This is a report on joint work with V. Melani.
One of the key constructions in the PTVV theory of shifted symplectic structures is the construction, via transgression, of a shifted symplectic structure on the derived mapping stack from an oriented manifold to a shifted symplectic stack vastly generalizing the AKSZ construction (which was formulated in the context of super manifolds). I will explain local-to-global approach to this construction, which also generalizes the construction to shifted Poisson structures and shows that the AKSZ/PTVV construction is compatible with quantization in a strong sense.
In the geometric models of matter, proposed in a joint paper with Michael Atiyah and Nick Manton, static particles like the electron or proton are modelled by Riemannian 4-manifolds. In this talk I will explain how the spin degrees of freedom appear in the geometric framework. I will also discuss a proposal for time evolution in one particular model, namely the Taub-NUT model of the electron.
Formal loop spaces are algebraic analogs to smooth loops. They were introduced and studied extensively in the 2000' by Kapranov and Vasserot for their link to chiral algebras.
In this talk, we will introduced higher dimensional analogs of K. and V. formal loop spaces. We will show how derived methods allow such a definition. We will then study their tangent complexes: even though formal loop spaces are "of infinite dimension", their tangent has enough structure so that we can speak of symplectic forms on them.
I will describe a functorial construction of the free BV-quantization of chain complexes equipped with antisymmetric forms of degree 1 in the context of infinity-categories. This is joint work with Owen Gwilliam.