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.
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.
Hamilton's equations, Poisson brackets, Canonical transformations
In general relativity, the picture of space–time assigns an ideal clock to each world line. Being ideal, gravitational effects due to these clocks are ignored and the flow of time according to one clock is not affected by the presence of clocks along nearby world lines. However, if time is defined operationally, as a pointer position of a physical clock that obeys the principles of general relativity and quantum mechanics, such a picture is, at most, a convenient fiction.
We present a new solution to the Hierarchy Problem utilizing non-linearly realized discrete symmetries. The cancelations occur due to a discrete symmetry that is realized as a shift symmetry on the scalar and as an exchange symmetry on the particles with which the scalar interacts. We show how this mechanism can be used to solve the Little Hierarchy Problem as well as give rise to light axions.
I will explain and state a conjecture of Kontsevich, that relates vertex models from statistical mechanics to En-algebras. I will also give the main ingredients of the proof of Kontsevich’s conjecture, which is a joint work in progress with Damien Lejay.
The based loop group is an inﬁnite-dimensional manifold equipped with a Hamiltonian action of a ﬁnite dimensional torus. This was studied by Atiyah and Pressley. We investigate the Duistermaat–Heckman distribution using the theory of hyperfunctions. In applications involving Hamiltonian actions on inﬁnite-dimensional manifolds, this theory is necessary to accommodate the existence of the inﬁnite order diﬀerential operators which aries from the isotropy representation on the tangent spaces to ﬁxed points. (Joint work with James Mracek)
Examples of Lie groups continued: SO(m,n), SU(n), Cartan subalgebra, proof of irreducibility of the adjoint representation for simple Lie groups.
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