I gave my talk at the AustMS 2009 meeting yesterday, and have now uploaded the PDF slides of my talk which was called Chromatic Roots and Maxmaxflow.
I was lucky enough to be the “keynote” speaker at the special session on Combinatorics so I got a one-hour time slot, which is usually easier to deal with than a shorter one.
The talk itself was a more focussed variant of a talk I gave at the British Combinatorial Conference in July this year, and describes my recent work with Alan Sokal, which is essentially complete, but just needs wrestling into final publishable shape. Working with Alan is a tremendous privilege, but exploring every possible generalization, hypothsis-weakening and related application that his incredibly fertile brain throws up is incredibly time-consuming for a mere mortal!
Anyway the gist of this work is that we want to find a parameter to replace maximum degree in the result that the moduli of chromatic roots are bounded by a function of maximum degree. The parameter maxmaxflow which is defined to be the maximum number of edge disjoint paths between any pair of vertices is a promising alternative, and this talk gives a very general overview of our proof that it works for series-parallel graphs.