Title: Counting Substructures in Hypergraphs with Spectrum
| Speaker | Krystal Guo |
| Affiliation | Korteweg-de Vries Institute for Mathematics, University of Amsterdam |
| Location | MC 6029 |
Abstract: Jacobi’s classical result expresses the generating function for closed walks at a vertex of a graph as the ratio of two characteristic polynomials. We find a hypergraph analogue of this relationship, showing that the same rational function for a hypergraph also counts combinatorial substructures within it, called infragraphs. We use Viennot’s Heaps of Pieces framework to establish this result for the adjacency tensor of a hypergraph. As an immediate consequence, we obtain an alternative proof for the monotonicity of the principal eigenvalue of a hypergraph. This is based on joint work with Joshua Cooper and Utku Okur (arXiv: 2411.03567).
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1:30pm.