Topology and geometry of networks and complexes

28^th March 2017, 13:00 Ashton Lecture Theater
Dr Ruben Sanchez-Garcia
Mathematical Sciences
University of Southampton
Southampton SO17 1BJ
United Kingdom

Abstract

Topological complexes, such as simplicial complexes, are combinatorial structures that encode topological and geometrical information of a continuous shape. They generalise networks to higher dimensions and, indeed, many of the standard analytical tools in network theory apply to complexes. One important example is the graph Laplacian, which is the 0-dimensional instance of a family of higher-dimensional combinatorial Laplacian operators on weighted simplicial complexes. In this talk, I will describe the mathematics behind this operator and how it may be used in practical applications, including digit recognition and ranking in horse racing.