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.
We give an introduction to the notion of moduli stack of a dg category.
We explain what shifted symplectic structures are and how they are
connected to Calabi-Yau structures on dg categories. More concretely,
we will show that the cotangent complex to the moduli stack of a dg
category A admits a modular interpretation: namely, it is isomorphic
to the moduli stack of the *Calabi-Yau completion* of A. This answers
a conjecture of Keller-Yeung. The talk is based on joint work
I will explain how to obtain the Gordon-Stafford construction and some related constructions of Z-algebras in the literature, using certain mathematical avatars of line defects in 3d N=4 theories. Time permitting, I will discuss the K-theoretic and elliptic cases as well.
In quantum geometric Langlands, the Satake equivalence plays a less prominent role than in the classical theory. Gaitsgory--Lurie proposed a conjectural substitute, later termed the fundamental local equivalence, relating categories of arc-integrable Kac--Moody representations and Whittaker D-modules on the affine Grassmannian. With a few exceptions, we verified this conjecture non-factorizably, as well as its extension to the affine flag variety. This is a report on joint work with Justin Campbell and Sam Raskin.
This is joint work with Justin Hilburn. We will explain a theorem showing that D-modules on the Tate vector space of Laurent series are equivalent to ind-coherent sheaves on the space of rank 1 de Rham local systems on the punctured disc equipped with a flat section. Time permitting, we will also describe an application of this result in the global setting. Our results may be understood as a geometric refinement of Tate's ideas in the setting of harmonic analysis.
We will review a set of conjectures related to the structure of cohomological Hall algebras (COHA) of categories of Higgs sheaves on curves. We then focus on the case of P^1, and relate its COHA to the affine Yangian of sl_2.
We describe an algorithm which takes as input any pair of
permutations and gives as output two permutations lying in the same
Kazhdan-Lusztig right cell. There is an isomorphism between the
Richardson varieties corresponding to the two pairs of permutations
which preserves the singularity type. This fact has applications in the
study of W-graphs for symmetric groups, as well as in finding examples
of reducible associated varieties of sln-highest weight modules, and
comparing various bases of irreducible representations of the symmetric
The velocity of a gravitational wave (GW) source provides crucial information about its formation and evolution processes.
Given a vector in a representation, can it be distinguished from zero by an invariant polynomial? This classical question in invariant theory relates to a diverse set of problems in mathematics and computer science. In quantum information, it captures the quantum marginal problem and recent bounds on tensor ranks. We will see that the general question can be usefully thought of as an optimization problem and discuss how this perspective leads to efficient algorithms for solving it.
We compute the path integral of three-dimensional gravity with negative cosmological constant on spaces which are topologically a torus times an interval. These are Euclidean wormholes, which smoothly interpolate between two asymptotically Euclidean AdS3 regions with torus boundary. From our results we obtain the spectral correlations between BTZ black hole microstates near threshold, as well as extract the spectral form factor at fixed momentum, which has linear growth in time with small fluctuations around it.