| Date |
Speaker |
Organization |
Title |
Abstract |
| February 9 |
Jason Manning |
University at Buffalo |
Geometric Dehn filling of high-dimensional hyperbolic manifolds |
I will describe a geometric Dehn filling construction on high dimensional
hyperbolic manifolds which gives lots of new examples of high
dimensional CAT(-1) and CAT(0) spaces with isolated flats. I will
describe the boundaries of these spaces and make some conjectures in
the context of group theoretic Dehn filling. This is joint work with Koji Fujiwara.
|
| February 16 |
Mohan Ramachandran |
University at Buffalo |
Solvable Kahler groups are virtually nilpotent |
We give a different proof of this result of Delzant.
|
| February 23 |
Xingru Zhang |
University at Buffalo |
Some Virtually Fibred hyperbolic 3-manifolds |
We give families of infinitely many closed hyperbolic
3-manifolds which are neither fibred nor semi-fibred, but are
virtually fibred. These appear to be the first known such families.
For an explicit example, all the 2m-fold (m>0) cyclic branched
covers of the 3-sphere branched over the knot 9_46 (which is the
(1/3, 1/3,-1/3)-Montesinnos knot) are such closed hyperbolic
3-manifolds. In fact this family contains infinitely many distinct
commensurable classes. We find such closed 3-manifolds by first
finding new families of virtually fibred cusped hyperbolic
3-manifolds, which are the complements of some Montesinos links in
the 3-sphere. This is a joint work with Steven Boyer.
|
| March 9 (Date changed!) |
Joseph Masters |
University at Buffalo |
Kleinian groups with ubiquitous surface subgroups |
We give examples of co-compact Kleinian groups with the property that
every finitely generated free subgroup is contained in a surface subgroup.
|
| March 23 |
Dror Bar-Natan |
University of Toronto |
Algebraic knot theory |
Wearing the hat of a topologist, I will argue that despite the
(justified) great interest in categorification, the good old
Kontsevich integral is even more interesting and understudied.
The gist: the Kontsevich integral behaves well under cool
operations that make a lot of 3 dimensional sense.
Transparencies of the talk are available
here.
|
| April 5 Thursday! |
Sreekrishna Palaparthi |
University at Buffalo |
A lower bound for the maximal cusp volume of a single cusped,
finite volume hyperbolic 3-manifold of tunnel number at-least 2.
|
I will present the following result of Colin Adams: " Let M be
a finite volume hyperbolic 3-manifold of one cusp. If the tunnel number
of M is greater than 1, then the volume in the maximal cusp of M is
at-least 3/4th of square root 3".
|
April 6 CANCELED |
Chris Hruska |
University of Wisconsin at Milwuakee |
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.
|
| April 13 |
Ben Klaff |
University of Texas at Austin |
Nonsolvable finite covers of hyperbolic knot complements |
I'll show how to combine the theory of character varieties over
fields of positive characteristic and estimates for the number of
points in algebraic curves over finite fields to find good upper
bounds for the smallest degree of a nonsolvable finite cover of a
hyperbolic knot complement. (This is joint work with P.B. Shalen.)
|
| April 20 |
Hiroshi Matsuda |
Columbia University |
A calculus on links via closed braids |
We improve "Markov Theorem Without Stabilization"
of Birman and Menasco.
|
| April 27 |
Genevieve Walsh |
Tufts University |
Commensurability classes of 2-bridge knots. |
Two three-manifolds are said to be commensurable if they share a
common finite-sheeted cover. We discuss commensurability classes of
knot complements, and prove that every hyperbolic two-bridge knot is
the unique knot complement in its commensurability class. This does
not hold for a general knot complement. For example, if a knot
complement admits a lens space filling, it is covered by another knot
complement. We speculate on the general case. This is joint work with
Alan Reid.
|