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 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.
In this talk, we'll discuss what it means to be a cohomology theory for topological stacks, using a notion of local symmetric monoidal inversion of objects in families. While the general setup is abstract, it specializes to many cases of interest, including Schwede's global spectra. We will then go on to discuss various examples with particular emphasis on elliptic cohomology. It turns out that TMF sees more objects as dualizable (or even invertible) than one might naively expect.
In this talk we will review various point-of-views on classical Chern-Simons theory and moduli of flat connections. We will explain how derived symplectic geomletry (after
Pantev-Toën-Vaquié-Vezzosi) somehow reconciles all of these. If time permits, we will discuss a bit the quantization problem.
Thanks to a result of Arinkin and Cāldāru, the derived self-intersection of a closed smooth subscheme of an ambiant scheme (over a field of characteristic zero) is a formal object if and only if the conormal bundle of the subscheme extends to a locally free sheaf at the first order. In this talk, we will explain a program as well as new results in order to describe these derived self-intersections in the non-formal case.
We give a definition of relative Calabi-Yau structure on a dg functor f: A --> B, discussing a examples coming from algebraic geometry, homotopy theory, and representation theory. When A=0, this returns the usual definition of Calabi-Yau structure on a smooth dg category B.