Algebra Seminar: Dancso -- Lattices and homological algebra

Zsuzsanna Dancso (University of Sydney) 

Friday 25 August, 12-1pm, Place: Carslaw 375 

Title: Lattices and homological algebra 

Abstract: I’ll begin with some dreams and motivation regarding lifting notions of
lattice theory to homological algebra.  For most of the talk, we’ll study a concrete
example: the lattices of integer cuts and flows associated to a finite graph.  Given a
graph G and choice of spanning tree T, we construct an algebra A(G,T) such that the
Groethendieck group of the category of finitely generated A(G,T)-modules with the Euler
(Ext) pairing contains the cut and flow lattices of G as orthogonal complements.  We’ll
discus many open problems regarding generalisations and possible uses for the extra
structure that is present at the category level, such as gradings.  Joint work in
progress with Anthony Licata.