Kazarian and Lando Seminars "Combinatorics of Vassiliev invariants": Speaker S.K.Lando

One of the main topics of the seminar are graph invariants (especially those of them that produce invariants of knots). Understanding of graph invariants requires understanding of the structure of graphs. One of the main features of graphs is the possibility to multiply them by considering their disjoint union. In addition, graphs can also be comultiplied, and together these two properties mean that graphs span a Hopf algebra. Graphs can be rather complicated, but the Hopf algebra of graphs contains a number of Hopf subalgebras spanned by subgraphs with relatively simple structure. Studying the behavior of various invariants for graphs in these subalgebras is instructive. A typical example is the well known chromatic polynomial of graphs.