Program

Open only to graduate students nominated by MSRI's Academic Sponsors Co-sponsored by MSRI and the Pacific Institute for the Mathematical Sciences. The mathematical theory of knots has become one of the most active areas of mathematics in the last few decades. Two important reasons for this are that many fields of mathematics (and physics) converge in the study of knots, and secondly there are applications to the study of manifolds as well as fields such as stereochemistry and molecular biology. This course will begin with an introduction to the subject, covering classical subjects such as the knot group, Seifert surfaces, Dehn surgery, branched coverings, Alexander polynomial as well as more recent work such as knot polynomials, skein theory, etc. The second week will be devoted to more specialized subjects such as hyperbolic goemetry in knot theory, quantum invariants, Vassiliev theory, representation theory and the Casson invariant. This course is intended for graduate students with some background in basic algebraic topology, including familiarity with the fundamental group, covering spaces, and homology theory. Some background in group theory and other basic algebraic concepts will also be assumed. LECTURERS: Colin Adams, Steve Boyer, Roger Fenn, Louis Kauffman, Dale Rolfsen, Susan Williams and others. A related, and overlapping, workshop on knot theory and 3-manifolds will be held at the Pacific Institute for the Mathematical Sciences on the UBC campus July 19-23. This PIMS event is also an MSRI-Network Conference. We acknowledge the generosity of the American Mathematical Society in providing for the students, at cost, the text 'Knots and Links' by Dale Rolfsen.