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.
Over the last few years it has become increasingly clear that there is a deep connection between quantum gravity and quantum information. The connection goes back to the discovery that black holes carry entropy with an amount given by the horizon area. I will present evidence that this is only the tip of the iceberg, and prove that a similar area law applies to more general Renyi entanglement entropies. To demonstrate the simplicity of this prescription, I will use it to calculate the mutual Renyi information between two disks of arbitrary dimension.
An important result in shifted symplectic geometry is the existence of shifted symplectic forms on mapping spaces with symplectic target and oriented source. I provide several examples of more complicated situations where stacks of maps shifted symplectic structures, or maps between them have Lagrangian structures. These include spaces of framed maps, pushforwards of perfect complexes, and perfect complexes on open varieties.
The High-Energy community is only now in the process of fully appreciating the opportunities the LHC provides by producing electroweak-scale resonances beyond threshold. On the one hand this is reflected by changing from the so-called 'kappa framework’ to effective operators and on the other hand by studying Higgs and gauge boson production in processes with large momentum transfer. Accessing more exclusive phase space regions will allow to either discover New Physics or improve Higgs-boson couplings measurements.
In many situations, geometric objects on a space have some kind of singular support, which refines the usual support. For instance, for smooth X, the singular support of a D-module (or a perverse sheaf) on X is as a conical subset of the cotangent bundle; similarly, for quasi-smooth X, the singular support of a coherent sheaf on X is a conical subset of the cohomologically shifted cotangent bundle. I would like to describe a higher categorical version of this notion.
The Todd class enters algebraic geometry in two places, in the Hirzebruch-Riemann-Roch formula and in the correction of the HKR isomorphism needed to make the Hochschild cohomology isomorphic to polyvector field cohomology (Kontsevich’s claim, proved by Calaque and van den Bergh). In the case of orbifolds the Riemann-Roch formula is known, but not the analogue of Kontsevich’s result. However, we can try to use the former as a guide towards a conjectural formulation for the latter.
I will discuss the comparison of shifted Poisson and symplectic geometry and applications to the shifted quantization of moduli spaces.
Let (X,w) be a -1-shifted symplectic derived scheme or stack over C in the sense of Pantev-Toen-Vaquie-Vezzosi with an "orientation" (square root of det L_X). We explain how to construct a perverse sheaf P on the classical truncation X=t_0(X), over a base ring A. The hypercohomology H*(P) is regarded as a categorification of X.
Now suppose i : L --> X is a Lagrangian in (X,w) in the sense of PTVV, with a "relative orientation". We outline a programme (work in progress) to construct a natural morphism
\mu : A_L[vdim L] --> i^!(P)
After the pioneering work of J. Lurie in [DAG-IX], the possibility of a derived version of analytic geometry drew the attention of several mathematicians. The goal of this talk is to provide an overview of the state of art of derived analytic geometry, addressing both the complex and the non-archimedean setting.