Combinatorial Laplacians on Acyclic Complexes
국웅 교수 (서울대학교)
2013. 10. 10.
The main topic of the talk is a determinantal formula for high dimensional
tree numbers of acyclic complexes via combinatorial Laplace operators
This result is a generalization of Temperley's tree number formula for
graphs, motivated by a simple (but not well-known) observation that
Temperley's method uses combinatorial Laplacian
in dimension zero. The talk will begin with a brief survey of properties
and applications of
including network theory and topological data analysis. Towards the
end, we will discuss a logarithmic version of the main formula of the
talk and demonstrate intriguing applications of its generating function
to various complexes that arise naturally in combinatorics.