Di. 05.11.2019, Oberseminar Algebra

Thema: Polynomials associated to graphs, matroids, and configurations. Referent: Prof. Dr. Mathias Schulze (TU Kaiserslautern), Raum: ENC-D 120, Zeit: 10:00 Uhr c.t.

Oberseminar Algebra

Polynomials associated to graphs, matroids, and configurations.

Dienstag, 05.11.2019, 10:00 Uhr c.t., Raum: ENC-D 120,

Referent: Prof. Dr. Mathias Schulze (TU Kaiserslautern)

Abstrakt:

Kirchhoff (Symanzik) polynomials are obtained from a graph as a sum of
monomials corresponding to (non-)spanning trees. They are of particular
importance in physics in the case of Feynman graphs. One can consider
them as special cases of matroid (basis) polynomials, or of configuration
polynomials. However the latter two generalizations differ in case of
nonregular matroids. This more general point of view has the advantage that
the classes of matroids and configurations are stable under additional
operations such as duality and truncation. In addition there are important
configuration polynomials, such as the second graph polynomial, which
are not of Kirchhoff type. I will give an introduction to the topic and
present new results relating the algebro-geometric structure of the singular
locus of configuration hypersurfaces to the underlying matroid structure.
Their proofs make essential use of matroid theory and, in particular, rely
on duality.