Date:	Mon, February 23, 2009
Time:	17:15
Place:	Research II Lecture Hall

Abstract: This theorem refers to finite type knot invariants, a theory discovered in the late 1980's independently by M. Goussarov in St.Petersburg and V. Vassiliev in Moscow. This theory produced a revolutionary impact on 3-dimensional topology; during the last 17 years, about 700 relevant publications appeared. Finite type invariants form an infinite-dimensional space, they can be defined in a very simple way and are stronger than all the known polynomial (or quantum) knot invariants. In this talk, we will give the definition of finite type invariants, explain a method to produce explicit formulas for such invariants (known as Polyak-Viro formulas) and speak about the Goussarov theorem which states that any finite type invariant can be produced by a formula of this kind. No knowledge of knot theory on the part of the listeners is presupposed.