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.
I will describe joint work with Sachin Gautam where we give a deﬁnition of the category of ﬁnite-dimensional representations of an elliptic quantum group which is intrinsic, uniform for all Lie types, and valid for numerical values of the deformation and elliptic parameters. We also classify simple objects in this category in terms of elliptic Drinfeld polynomials. This classiﬁcation is new even for sl(2), as is our deﬁnition outside of type A.
SU(2) and SU(3) tensors, Young's tableau.
Various recent developments, in particular in the context of topological Fukaya categories, seem to be glimpses of an emerging theory of categoriﬁed homotopical and homological algebra. The increasing number of meaningful examples and constructions make it desirable to develop such a theory systematically. In this talk, we discuss a step towards this goal: a categoriﬁcation of the classical Dold–Kan correspondence
Hamiltonian vector flows, Hamilton's function, Liouville's theorem, Hamilton-Jacobi equation
In this talk I will present some upcoming work on Bridgeland stability conditions on partially wrapped Fukaya categories of topological surfaces. The main result is a proof that the stability conditions defined by Haiden, Katzarkov and Kontsevich using quadratic differentials cover the entire stability space. This proof uses a definition of the new concept of relative stability conditions, which is a relative version of Bridgeland's definition, with functorial behavior analogous to compactly supported cohomology.
The role of coherence in quantum thermodynamics has been extensively studied in the recent years and it is now well-understood that coherence between different energy eigenstates is a resource independent of other thermodynamics resources, such as work. A fundamental remaining open question is whether the laws of quantum mechanics and thermodynamics allow the existence a "coherence distillation machine", i.e. a machine that, by possibly consuming work, obtains pure coherent states from mixed states, at a nonzero rate.
There are various ways to define factorization algebras: one can define a factorization algebra that lives over the open subsets of some fixed manifold; or, alternatively, one can define a factorization algebra on the site of all manifolds of a given dimension (possibly with a specified geometric structure). In this talk, I will outline a comparison between G-equivariant factorization algebras on a fixed model space M to factorization algebras on the site of all manifolds equipped with a (M, G)-structure, given by an atlas with charts in M and transition maps given by elements of G.
This talk is based on joint work with Yuri Manin. The idea of a “geometry over the ﬁeld with one element F1” arises in connection with the study of properties of zeta functions of varieties deﬁned over Z. Several diﬀerent versions of F1 geometry (geometry below Spec(Z)) have been proposed over the years (by Tits, Manin, Deninger, Kapranov–Smirnov, etc.) including the use of homotopy theoretic methods and “brave new algebra” of ring spectra (To¨en–Vaqui´e).
Killing metric, Coset manifold, Representation theory of SU(2) Lie algebra, SU(2) tensors.
I will review the construction of “higher operations” on local and extended operators in topological ﬁeld theory, and some applications of this construction in supersymmetric ﬁeld theory. In particular, the higher operation on supersymmetric local operators in a 3d N=4 theory turns out to be induced by the holomorphic Poisson structure on the moduli space of the theory.
Check back for details on the next lecture in Perimeter's Public Lectures Series