Keynote Speaker
William Menasco
University at Buffalo
Title:
The geometry of the curve complex.
Abstract:
Let S_g be a closed oriented surface of genus g \geq 2 and
C^1(S_g) be its curve complexvertices are
homotopy classes of essential simple closed curves with two
vertices sharing an edge if they have disjoint
representatives. In this talk we will survey some of the results
on the coarse geometry of the curve complex: that
C^1(S_g) is path connected; that the vertices,
C^0(S_g), have a natural metric; that this metric on
C^0(S_g) is unbounded; and, that this metric on
C^0(S_g) is deltahyperbolic. Finally, we will
talk about recent results of BirmanMargalitM on an algorithm
for computing distance in C^0(S_g).
Keynote Speaker
Nataša Jonoska
University of South Florida
Title:
How biology can incite new ideas in algebra and topology
Abstract:
In the last couple of decades, it has become evident that
algebraic and topological approaches are well suited for modeling
certain biological processes. The specificities of processes in
molecular biology have required mathematicians to look into
notions and problems that might not have been considered before
and have brought new mathematical ideas. We will start with one of
Tom Head’s pioneering concepts on splicing systems showing
connections between DNA recombinant processes and formal language
theory. Then we will discuss how some concepts in
spatial/topological graph theory have developed from modeling DNA
rearrangements.

Keynote Speaker
JeanFrançois Lafont
Ohio State University
Title:
Totally geodesic submanifolds in closed hyperbolic manifolds
Abstract:
I will briefly describe the various constructions of closed
hyperbolic manifolds, with a focus on the arithmetic
vs. nonarithmetic dichotomy. I will then illustrate this
dichotomy by discussing two results on the structure of
submanifolds inside these manifolds.
Keynote Speaker
Ruth Charney
Brandeis University
Title:
A geometric approach to Artin groups
Abstract:
Artin groups arise naturally as fundamental groups of hyperplane
complements. They form a large and diverse collection of groups
which include braid groups, free groups, free abelian groups and
many more. While some classes of Artin groups are well understood,
many remain mysterious, with even very basic questions
unanswered. In this talk I will explain why Artin groups are
interesting and review what is known and not known about these
groups. I will then discuss some geometric techniques for studying
these questions (including some recent joint work with Rose
MorrisWright).
