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Online, School of Mathematics and Statistics, University of Sydney

The area of integrable systems lies at the intersection of mathematics and physics. This workshop brings together speakers on topics such as integrable systems, special functions, mathematical physics, discrete dynamical systems, and Painlevé equations.

This will be the 9th workshop organised by the Integrable Systems Group, organised by Nalini Joshi, Sean Gasiorek and Milena Radnovic. For a tentative list of speakers and further information, visit the workshop webpage.

Online: Zoom registration

Abstract: On fundamental groups, the discriminant ∏_i≠k(z_i – z_k) ∈ ^× of a finite collection of points of the plane defines the abelianization homomorphism sending a braid to its number of overcrossings less undercrossings or writhe. In terms of diffeomorphisms of the punctured plane, it defnes a kind of `invertible topological quantum field theory’ associated to the Burau representation, and in the classical physics of point particles the real part of its logarithmic derivative is the potential energy of a collection of Coulomb charges, while its imaginary part is essentially the Nambu-Goto area of a loop of string in the three-sphere. Its higher homotopy theory defines a very interesting a double-loop map
× Ω<sup>2</sup>S<sup>3</sup> → 𝒫ic(S<sup>0</sup>)
to the category of lines over the stable homotopy ring-spectrum, related to Hopkins and Mahowald’s exotic (E2) multiplication on classical integral homology, perhaps related to the `anyons’ of nonclassical physics.

Bio: Jack Morava graduated with a PhD from Rice University in 1968, followed by an Academy of Sciences postdoc in Moscow with Yuri Manin and Sergei Novikov. He joined the Johns Hopkins faculty in 1979 where he was involved in the Japan-US mathematical institute, and from roughly 2003 to 2010 he worked half-time on the DARPA FunBio initiative, before retiring in 2017.