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Department of Mathematics |
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See my new webpage.
Welcome!
I just finished my PhD in the mathematics department at Cornell University, where my advisor was John H. Hubbard. I will spend 2008-2009 in Europe at the University of Warwick as an NSF postdoc. From 2009-2013, I will be at Harvard University as a Benjamin Peirce assistant professor/NSF postdoc. I spent 2006-2007 studying in Marseille, France, where I wrote a different thesis and became a docteur de mathématiques with a doctorate from the Université de Provence in May 2007.
Research:
My research involves a brand new connection between
Teichmüller theory and complex dynamics that arose from a special construction in the solution of
the "twisted rabbit" problem. Inspired by Thurston's theorem of the characterization of rational maps,
John H. Hubbard posed the twisted rabbit problem about 25 years ago; this problem was recently
solved
by Laurent Bartholdi and Volodia
Nekrashevych using iterated monodromy groups in this paper.
Papers: Slow matings and twisted matings, (with X. Buff, A. Epstein, J.
H.
Hubbard), in preparation
Teichmüller theory and endomorphisms of $\P^n$,
in preparation
On Thurston's Pullback Map, (with X. Buff, A. Epstein, K. Pilgrim), to appear in: Complex Dynamics,
Families and Friends, in honor of John H. Hubbard's 60th Birthday
SaddleDrop: a tool for studying dynamics in $\C^2$,
submitted
Movies:
Links:
A key part of their solution contains the construction of a map on a certain moduli space. My
research focuses on generalizing this construction, which leads to very interesting maps. For example,
in
some cases, these maps extend to post-critically finite endomorphisms of complex projective space; the
methods
in my French thesis provide a new and systematic way to generate them. We can exploit the fact that these
maps were found in the context of Teichmüller theory, providing a wealth of tools with which to
understand their dynamics. These maps have also led to a deeper
understanding
of some of the
Teichmüller theory involved.
Calculating the iterated monodromy group of a
map on $\P^2$, (with J. Belk), in preparation
This research has led to "slow matings". We form a skew product where the
base map is the map on moduli space, and the map in the fiber is a
rational map on $\P^1$. If we look in the fiber of this
skew product we see evidence of slow mating for some special examples. To see some movies of slow mating,
look
here. For a
more detailed explanation, see the paper 'Slow matings and twisted matings.'
Dynamics seminar
fun photos
pendulum 1