Saturday, December 9, 9AM-12:15PM
Bromfield-Pearson, Room 101
We will provide coffee and bagels,
starting at 9AM.
The Dowling Garage is $8.
Alternatively, there is metered parking on Boston Ave.
and in the lot at 574 Boston Ave. which is not checked
on the weekends.
9:30-10:15: Tarik Aougab
Title: Covers, curve complexes, and hyperbolic
Abstract: Let X be a closed orientable surface of
genus at least 2. The curve complex of X is a
simplicial complex that encodes the combinatorics of
how simple closed curves intersect on X. In this talk,
we'll introduce the curve complex and discuss its
connections to hyperbolic 3-manifolds and to
Teichmuller theory. The goal will be to state a result
relating covering spaces of X to the geometry of its
curve complex, and to give a rough idea of how the
proof uses hyperbolic geometry. This represents joint
work with Priyam Patel and Sam Taylor.
Michael Ben-Zvi (Tufts)
Title: Boundaries of hyperbolic and CAT(0)
Abstract: In the land of hyperbolic
groups, there are important connections
between algebraic properties of the group
and topological properties of the visual
boundary. We will discuss some of these
result, in particular a major result which
says hyperbolic groups which do not split
over finite groups have connected and
locally connected boundaries, and hence
path connected boundaries. For CAT(0)
groups, the connections are less clear. We
will address some of the questions we
might want to ask about CAT(0) groups and
their boundaries and partially answer
Title: Dynamics on M_2: square-tiled surfaces,
Teichmuller curves and modular curves.
Abstract: In my talk I will address a basic question
about topological branched covers. Call two finite
covers over a torus branched over a single point of
the same type, if there is an orientation preserving
homeomorphism of the torus that lifts to the
homeomorphism of the covers. How many types of covers
of fixed genus and degree are there? The answer to
this naive question is not known in the simplest case
of genus 2.
Closer investigation of this question will bring us to
the notions of square-tiled surfaces and Teichmuller
curves. I will also define a flat conformal metric on
the modular curve X(d), in which it decomposes into
unit squares identified along parallel sides, and show
how does it help to answer the main question. In
particular, we will see “pagoda" structures of X(d)
that arise in the case of prime d.