Topic 
Speaker and Date 
Details 
Dependencies

Reidemeister's theorem 
Lior Zaibel, March 18th 
Prove that any two diagrams for the same knot are connected by a
sequence of Reidemeister moves. See almost any book on knot theory.

None. 
Linking and selflinking numbers 

The simplest measurement of the linking of a two component link and its
problemmatic nature in the case of a single component knot. See almost
any book on knot theory.

None. 
Seifert surfaces and knot factorization 
Ittai Chorev, April 29th 
Knots are like integers  there is a "product", there are "primes", and
there is "unique factorization". See Lickorish's book.

None. 
The Kauffman bracket and the Jones polynomial 
Yossi Regev, April 15th 
These are very simple and very powerful knot invariants. See almost any
modern book on knot theory.

None. 
Khovanov's categorification of the Jones polynomial 

A new and very surprising extension of the Jones polynomial using
homological algebra. Hot but difficult! See my paper On Khovanov's
Categorification of the Jones Polynomial.

The Jones polynomial 
The geometry of alternating links 
Tom Erez, June 10 
These are links whose diagrams alternate updownupdown... They are
particularly well behaved. See Lickorish's book.

Seifert surfaces and factorization 
The Jones polynomial of alternating links 
Tomer Avidor, May 6 
See Lickorish's book.

The Jones polynomial 
The Alexander polynomial 

A classical invariant deeply rooted in algebraic topology. See
Lickorish's book and many other sources.

Seifert surfaces, linking numbers. 
The fundamental group 

The fundamental group of a knot complement is an extremely strong
invariant of the knot, it's easy to compute, but... See any book on
knot theory.

None. 
Surgery and 3manifolds 

This is one of the fundamental links between knot theory and "higher"
3dimensional topology; every 3manifold comes from a knot in some way!
See Lickorish's book and many other sources.

None. 
Finite type invariants and weight systems 

These are knot invariants that behave as if they are polynomials on the
the space of all knots. They seem very strong, but nobody really knows
how strong they are. See my paper On the Vassiliev knot
invariants and many further sources in VasBib.

None, but the Jones or Alexander polynomials are helpful. 
Weight systems and Lie algebras 

One reason why finite type invariants are so interesting is that
they are intimately connected to Lie algebras (via their weight
systems). See my paper On the Vassiliev knot
invariants and many further sources in VasBib.

Finite type invariants 
The second hull of a knotted curve 
Aviv Sheyn, May 27 
Every knot defines a "deep inside" part of space which is "surrounded"
by the knot more than just once. See SecondHull.gif and the article The
Second Hull of a Knotted Curve by Cantarella, Kuperberg, Kusner and
Sullivan.

None 
Braids and knots 
Yishai Fried, June 24 
The theorem stating that every knot is the closure of a braid and
Markov's theorem, a complete description of knots in terms of braids.
See the PrasolovSossinsky book.

None 