Extending graph invariants to embedded graphs

Date:

Time:

2021 10 18

15:30 (GMT+0)

Speaker:

Sergei Lando

Knots and representation theory

The classical approach (developped by B.Bollobas, O.Riordan, and many others)
to extending graph invariants to embedded graphs consists in enhancing the
invariants by implementing in them information about the embedding of a graph
into a surface. The talk will be devoted to another approach, which is based on
the Hopf algebra structures on spaces of graphs, chord diagrams modulo 4-term
relations, and delta-matroids. The approach proved to be efficient, and it allows
one to extend to embedded graphs such invariants as the degeneracy of a graph,
the number of signed Hamiltonian cycles, skew characteristic polynomial, and the
Stanley symmetrized chromatic polynomial.

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