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 decade, there have been enormous gains in machine learning technology primarily driven by neural networks. A major reason neural networks have outperformed older techniques is that the cost of optimizing them scales well with the size of the training dataset. But neural networks have the drawback that they are not very well understood theoretically.
In this talk we will discuss three (intimately related) examples of 4-manifold invariants based on higher structures:
- VOA[M4] from transgression of EFTs;
- SW and Donaldson invariants as chiral algebra correlators;
- Massey triple products from trisections.
These topics are based, respectively, on work with A.Gadde, P.Putrov (and work to appear with B.Feigin); recent paper with M.Dedushenko and P.Putrov; and a solo paper of the speaker.
Skew Howe duality is based on a very simple observation: the set of n by m matrices has commuting action of SL_n and SL_m. We can use this observation to study morphisms of GL_m representations using GL_n. This perspective has proven very useful in recent years for studying quantum knot invariants and their categorifications. I will survey work in this direction from the last 10 years, including more recent developments concerning annular skew Howe duality and annular knot invariants.
In this talk, intended for a broader audience, I promise to use techniques only at the level of university calculus. While staying at this level, our goal will be to learn conceptual lessons for categorification of quantum group invariants of knots and 3-manifolds, also known as the Witten-Reshetikhin-Turaev (or WRT) invariants. In particular, we will introduce new q-series invariants of 3-manifolds that have integer powers and integer coefficients and, if time permits, discuss their various constructions and properties. The talk is based on several papers with D. Pei and/or P. Putrov, C.
Abstract TBA
Polyakov’s bootstrap programme aims at solving conformal field theories using
unitarity and conformal symmetry. Its implementation in two dimensions has been
highly successful and numerical studies, in particular of the 3-dimensional Ising
model, have clearly demonstrated the potential for higher dimensional theories.
Analytical results in higher dimensions, however, require significant insight
into the conformal group and its representations. Surprisingly little is actually
Ultralight bosons can induce superradiant instabilities in spinning black holes, tapping their rotational energy to trigger the growth of a bosonic condensate.
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