Algebraic Geometry Seminar

Thurston Vanishing

Speaker: Michael McQuillan, University of Rome

Location: Warren Weaver Hall 512

Date: Tuesday, October 3, 2023, 3:30 p.m.


Thurston's method of proof in establishing that rational maps
$f$ of $\mathbb{P}^1_{\mathbb{C}}$ with pre-periodic critical points which
aren't multiplication on an elliptic curve $\pm 1$ are rigid was generalised
by Adam Epstein to an almost exhaustive local to global theory of deformations
of dynamical systems. Indeed arguably its only fault was not to have
identified a suitable topus of $f$-equivariant sheaves. Once one remedies
this lacuna, natural extensions of Epstein's methods and new results in
dynamical systems immediately suggest themselves. En passant we calculate
the dualising complex of a real blow up, which is not only a sheaf but
a remarkably algebraic one which presents notable opportunities for
trivialising the analysis of Stokes' phenomenon. An IHES pre-print with
the same title ought to be available before the talk.