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.
Given a quiver with potential, Kontsevich-Soibelman constructed a Hall algebra on the cohomology of the stack of representations of (Q,W). In particular cases, one recovers positive parts of Yangians as defined by Maulik-Okounkov. For general (Q,W), the Hall algebra has nice structure properties, for example Davison-Meinhardt proved a PBW theorem for it using the decomposition theorem.
Since the 1980s, mathematicians have found connections between orbit closures in type A quiver representation varieties and Schubert varieties in type A flag varieties.
Neutrinos are a key (although implicit) ingredient of the standard cosmological model, LambdaCDM. Firstly, neutrinos directly participate in neutron freeze out during BBN, and secondly, they represent 40% of the energy density of the Universe after electron positron annihilation up to almost matter radiation equality. The latter fact makes neutrinos a necessary element to understand CMB observations.
In this talk, I will give a geometric description of the category of representations of the centralizer of a regular unipotent element in a reductive algebraic group in terms of perverse sheaves on the Langlands dual affine flag variety. This is joint work with R. Bezrukavnikov and S. Riche.
Neural networks (NNs) normally do not allow any insight into the reasoning behind their predictions. We demonstrate how inﬂuence functions can unravel the black box of NN when trained to predict the phases of the one-dimensional extended spinless Fermi-Hubbard model at half-ﬁlling. Results provide strong evidence that the NN correctly learns an order parameter describing the quantum transition.
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.