| Date |
Speaker |
Organization |
Title |
Abstract |
| August 31st |
No Speaker |
|
Organizational meeting |
|
| September 7th |
Jason Fox Manning |
University at Buffalo
|
Residual finiteness and separability of quasi-convex subgroups. |
I'll describe some recent work with Ian Agol and Daniel Groves applying relatively hyperbolic Dehn filling to questions about the profinite topology on hyperbolic groups. |
| September 14th |
Jason Fox Manning |
University at Buffalo |
Residual finiteness and separability of quasi-convex subgroups, Part II. |
|
| September 21st |
Matthew Buettgens |
University at Buffalo |
Computing the L2 Alexander Invariant for knots. |
The L2 Alexander invariant of a knot defined by Weiping Li and Weiping Zhang is a potentially useful tool for addressing the
hyperbolic volume conjecture and has led to a generalization of that conjecture. If the parameter t of this invariant is set to a
number of modulus 1, the result is scaled hyperbolic volume. Otherwise, we know of no computations of this invariant that have
been performed, except for very small and very large values of t, which are trivial. We present an efficient new algorithm for
computing these invariants--and related computations such as group-ring Mahler measures and Fuglede-Kadison determinants--up to
any desired degree of accuracy. Along the way, we will give an introduction to harmonic analysis on infinite Cayley graphs.
|
| September 28th |
No seminar. |
|
|
|
| October 5th |
Dani Wise |
McGill University |
Nonpositively Curved Cube Complexes in Geometric Group Theory |
Nonpositively curved cube complexes have come to occupy an
increasingly important role in geometric group theory. Surprisingly many
of the groups traditionally studied by combinatorial group theorists are
turning out to act properly on CAT(0) cube complexes. This is leading to
an increased and more unified understanding of these groups, as well as the
resolution of some of the algebraic problems that were first raised in
combinatorial group theory but were unapproachable without geometric
methods. We will survey groups acting on CAT(0) cube complexes with an eye
towards these recent developments.
|
| October 12th |
Chris Hruska |
University of Wisconsin - Milwaukee |
Relative hyperbolicity of countable groups |
Hyperbolic groups have been a central topic in geometric group theory
since they were introduced by Gromov in the 1980s. However certain
groups exhibit aspects of hyperbolicity without actually being
hyperbolic groups. For instance free products A*B, and fundamental
groups of finite volume hyperbolic manifolds. These are examples of
relatively hyperbolic groups.
The notion of a relatively hyperbolic group G was introduced by
Gromov, and later by Farb--Bowditch using a substantially different
definition. When
G is finitely generated, Bowditch showed that these two definitions
are equivalent. I have recently proved that they are equivalent for
all countable groups G. I will discuss this equivalence (which uses
techniques of Groves--Manning). I will also explain several ways that
nonfinitely generated relatively hyperbolic groups arise "in
nature".
|
| November 16th |
Scott Williams |
University at Buffalo |
The Box Product problem |
Suppose the product of countably many copies of the reals is given the
box topology. Can disjoint closed sets be separated by a continuous
function?
This eighty year old problem has captivated many topologists and
logicians. We present some history of this problem.
The generalized problem asks this question for the classes of spaces X
for which the answer is "yes."
We present the solution to the generalized problem.
|
| November 23rd |
No seminar (Fall Recess) |
|
|
|
| November 30th |
Scott Williams |
University at Buffalo |
The Box Product problem, part 2 |
|
| December 7th |
Kathleen Petersen |
Queen's University |
Character Varieties of Twist Knots |
It's well known that the canonical component of the SL(2,C)
character variety for the figure-eight knot complement is an elliptic
curve. I'll prove that the other hyperbolic twist knots correspond to
hyperelliptic curves and compute the genus of these curves.
(joint with Ronald van Luijk and Melissa Macasieb)
|
Old seminars: