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.
![](http://stream.math.snu.ac.kr/lecture/each2013/img_ab/ab_19.gif)
![](http://stream.math.snu.ac.kr/lecture/each2013/img_ab/ab_20.gif)
![](http://stream.math.snu.ac.kr/lecture/each2013/img_ab/ab_19.gif)