Algebra Seminar: Nir Gadish -- Letter-braiding invariants of words in groups

Nir Gadish (University of Michigan) will be speaking in the algebra seminar in two
weeks.  We will go out for lunch after the talk.  

When: June 7 May, 12-1pm 

Where: SMRI seminar room (Macleay Building (A12) room 301) 

Title: Letter-braiding invariants of words in groups.  

Abstract: How can we tell if a group element can be written as k-fold nested commutator?
I suggest seeking computable invariants of words in groups that detect k-fold
commutators.  We introduce the novel theory of letter-braiding invariants - these are
elementarily defined functions on words, inspired by the homotopy theory of loop-spaces
and carrying deep geometric content.  They give a universal finite-type invariant for
arbitrary groups, extending the influential Magnus expansion of free groups that already
had countless applications in low dimensional topology.  As a consequence we get new
combinatorial formulas for braid and link invariants, and a way to linearize
automorphisms of general groups that specializes to the Johnson homomorphism of mapping
class groups.