03.11.2008, Topics in Topology Sergei Chmutov (Ohio St. U./MPI): Combinatorics of the HOMFLY polynomial I'll discuss the Gauss diagram approach to Vassiliev invariants coming from the HOMFLYPT polynomial. This approach allows to define HOMFLY polynomial for virtual links with ordered components and with a based point on each component. Also it leads to the Gauss diagram formulas for the Taylor coefficients of the HOMFLY polynomial. This is a joint work with Michael Polyak.