An application of Computational Homology to the Ising Model

Abstract: Homology groups were developed in algebraic topology as a way of distinguishing objects by counting their holes. Recently, computers and algorithms have improved to the point where it is efficient to compute the homology of arbitrary data. This is being used in a wide variety of applications to study real world systems. Here, we develop the basic theory of homology on cubical sets. We then look at an application of this tool in studying the Ising model. We assume no prior knowledge beyond basic group theory.

combinatoricscomplex variablesfunctional analysisgeneral mathematicsgroup theoryK-theory and homologynumber theoryoperator algebrasprobabilityquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the discipline

GAG seminar

Series comments: Description: Non-specialized research seminar