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

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/