SMRI Seminar: Robertson, M -- Expansions, completions and automorphisms of welded tangled foams

**REMINDER - SEMINAR TOMORROW (THURSDAY)**

’Expansions, completions and automorphisms of welded tangled foams’ 
Marcy Robertson (University of Melbourne) 

When: Thursday 22 April, 3.30pm - 4.30pm (AEST) 
Where: Quad S227 (University of Sydney staff, students & affiliates) 
and via Zoom (register here https://bit.ly/3cYpCdh) 

Abstract: Welded tangles are knotted surfaces in R^4. Bar-Natan and Dancso described a
class of welded tangles which have "foamed vertices" where one allows surfaces to merge
and split.  The resulting welded tangled foams carry an algebraic structure, similar to
the planar algebras of Jones, called a circuit algebra. In joint work with Dancso and
Halacheva we provide a one-to-one correspondence between circuit algebras and a form of
rigid tensor category called "wheeled props." This is a higher dimensional version of
the well-known algebraic classification of planar algebras as certain pivotal
categories.  
This classification allows us to connect these "welded tangled foams,"
to the Kashiwara-Vergne conjecture in Lie theory. In work in progress, we show
that the group of homotopy automorphisms of the (rational completion of) the
wheeled prop of welded foams is isomorphic to the group of symmetries KV, which
acts on the solutions to the Kashiwara-Vergne conjecture. Moreover, we explain
how this approach illuminates the close relationship between the group KV and the
pro-unipotent Grothendieck--Teichmueller group.

Bio: Marcy Robertson obtained her PhD in Algebraic Topology from the University of
Illinois at Chicago in 2010.  From there she worked in Canada, France and her native
United States before settling down in Australia 2015. She is now a Senior Lecturer of
Pure Mathematics at the University of Melbourne.


Note - those attending in-person are invited to join us for afternoon on the SMRI 
terrace, prior to the seminar, at 3:00pm. Please email smri.admin@sydney.edu.au to RSVP