Algebraic Geometry Seminar
Andrei Caldararu
University of Wisconsin
A spectral sequence from the ribbon graph bicomplex
Abstract: The ribbon graph complex has been studied intensely in the past 15 years,
in part due to Kontsevich's success using it to prove Witten's conjecture. While
being a very simple combinatorial object, it encodes data about a complicated
object, the mapping class group of surfaces, which in turn completely encodes all
the topological information about moduli spaces of curves. Tom Bridgeland observed
that there exists a second differential on the space of all graphs, and in work
with Junwu Tu we proved that this differential, along with the old one, makes the
space of ribbon graphs into a bicomplex. In my talk I shall discuss this bicomplex,
and state a conjecture about the degeneration of the associated spectral sequence.
If time allows, I'll try to speculate on the techniques to prove this conjecture,
and digress on potential applications.
Friday December 5, 2008 at 4:30 PM in SEO 636