Type: Seminar

Distribution: World

Expiry: 11 Nov 2021

CalTitle1: SMRI Algebra and Geometry Online - Morava -- On the group completion of the Burau representation

Auth: hannahb@staff-10-48-26-27.vpnuser.sydney.edu.au (hbry8683) in SMS-SAML

SMRI Algebra and Geometry Online ’On the group completion of the Burau representation’ Jack Morava (Johns Hopkins University) Thursday 11th November 10:00am-11:30am (AEDT) Register: https://uni-sydney.zoom.us/meeting/register/tZUvduCspjMrHNA5A9-ejSBqX2NXmESSjZJX Abstract: (based on joint work with D Rolfsen) On fundamental groups, the discriminant \prod_{i \neq k} (z_i - z_k) \in \C^\times 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 defines 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 \Z \times \Omega^2 S^3 \to \Pic(S^0) to the category of lines over the stable homotopy ring-spectrum, related to Hopkins and Mahowald’s exotic (E_2) multiplication on classical integral homology, perhaps related to the `anyons’ of nonclassical physics. Biography: Jack Johnson Morava, of Czech and Appalachian descent, studied under Eldon Dyer and Sir Michael Atiyah, graduating 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. He retired in 2017 to live with his anthropological linguist wife in Charlottesville, Virginia and get some work done. Note: These seminars will be recorded, including participant questions (participants only when asking questions), and uploaded to the SMRI YouTube Channel https://www.youtube.com/c/SydneyMathematicalResearchInstituteSMRI Other upcoming SMRI events can be found here: https://mathematical-research-institute.sydney.edu.au/news-events/

Calendar (ICS file) download, for import into your favourite calendar application

UNCLUTTER for printing

AUTHENTICATE to mark the scnews item as read