The Second Miniconference on Knot Theory and its Ramifications
will be held on Saturday, March 30, 1996 at the George
Washington University.

10:30 - 11:30   Ken Millett, Physical Knots
Abstract. I would discuss results on polygonal knots, knot energies,
and thickness of knots.

12:00 -  1:00   Jeff Weeks, What is a hyperbolic knot?
The talk will give a gentle introduction to the theory
of hyperbolic knots.  The computer program SnapPea will
illustrate the main ideas.

2:30 -  3:30  Wilbur Whitten, Knot inversion and the isometry groups
                               of hyperbolic 3-manifolds
The problem of deciding whether a given knot K in the 3-sphere is
invertible is shown to be equivalent to deciding when two knot groups are
isomorphic.  These are the groups
of two satellite knots formed with K as their (only) maximal companion, and
each of these satellite knots is itself noninvertible regardless of the
invertibility status of K.  This result shows clearly why the invertibility
question of a knot is generally so difficult and it coincidently leads to
three conjectures (too lengthy to include in this abstract)
concerning ths isometry groups of the hyperbolic 3-manifolds obtained
by surgery on hyperbolic links.  If these conjectures are correct, such
an isometry group would be one of a well-defined finite collection.

3:45 -  4:10  Yongwu Rong, Introduction to Higher Order Link Polynomials
Two major link invariants are Homfly+PT polynomial
and the Vassiliev invariants.  We introduce what we call ``higher
order link polynomials'' that combine ingredients from both.
We carry out a detailed study for the order one polynomials.
Various possible applications will be discussed.

4:20 -  4:45  Jozef H. Przytycki, What is new in skein modules?
Skein modules are the basic objects of algebraic topology based on knots
(as homology and homotopy groups are the basic objects of a classical
algebraic topology). The last half a year brought big progress in the
theory (which is 9 years old). It will be illustrated by an example
of detecting torsion in the Kauffman bracket skein modules using
an SL(2,C) character variety and hyperbolic geometry.

4:55 -  5:20  Adam Sikora, Skein algebra of a handlebody from the
                            point of view of algebraic geometry
    This talk will be mainly concerned with a non-standard 'algebraic topology'
built on knots. In particular, we will define {\it the Kauffman bracket skein
module} $S(M)$, a module associated to any 3-dimensional manifold $M$.
A particular version of this module has a structure of a commutative algebra
and therefore it is called a {\it skein algebra}. The skein algebra depends
only on the fundamental group of a manifold.
     We are going to investigate skein algebras using methods of algebraic
geometry. In particular, we will show how the skein algebra associated to a
manifold $M$ is connected with a {\it character variety}, an algebraic set
representing all traces of homomorphisms of $\pi_1(M)$ into $Sl_2(C)$.
This will give a very nice geometric interpretation of character varieties,
which essentially have been investigated since the time of Poincare, Fricke
and Klein.

5:30 - 5:50   Michael McDaniel, Cablings of Vassiliev Invariants
We will study Vassiliev Invariants coming form cabling and
describe a practical way of calculating them.

Local Organizers: Jozef H. Przytycki e-mail: przytyck@math.gwu.edu
                           Yongwu Rong        e-mail: rong@math.gwu.edu