David Cimasoni : Covering spaces and spanning trees

Abstract: The aim of this talk is to show how basic notions traditionally used in the study of "knotted embeddings in dimensions 3 and 4", such as covering spaces and representation theory, can have non-trivial applications in combinatorics and statistical mechanics. For example, we will show that for any finite covering G′ of a finite edge-weighted graph G, the spanning tree partition function on G divides the spanning tree partition function on G′ (in the polynomial ring with variables given by the weights). Setting all the weights equal to 1, this implies a theorem known since 30 years: the number of spanning trees on G divides the number of spanning trees on G′. Other examples of such results will be presented.
Joint work (in progress) with Adrien Kassel.

Recording during the thematic meeting "Knotted Embeddings in Dimensions 3 and 4" the February 15, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France)

Filmmaker: Guillaume Hennenfent

- Chapter markers and keywords to watch the parts of your choice in the video
- Videos enriched with abstracts, bibliographies, Mathematics Subject Classification
- Multi-criteria search by author, title, tags, mathematical area