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Cohomology, symbolic dynamics and operator algebras

Grant


Scheme


  • Discovery Projects

Abstract


  • This project is in pure mathematics, broadly in the area of functional analysis, and more specifically in operator algebras. It will investigate novel connections between topological higher-rank graphs, multidimensional symbolic dynamics, cohomology theory and operator algebras. We will first study how topological graphs and their analogues can provide new and powerful visual models for the classical theory of continuous-trace C*-algebras and Fell algebras. We will build on this to develop cohomological and C*-algebraic techniques for higher-rank symbolic dynamics and to pioneer an intriguing new field of study at the nexus of three very active areas of mathematics: cohomology, symbolic dynamics and operator algebras.

Date/time Interval


  • 2012 - 2015

Sponsor Award Id


  • DP120100389

Local Award Id


  • 101489

Scheme


  • Discovery Projects

Abstract


  • This project is in pure mathematics, broadly in the area of functional analysis, and more specifically in operator algebras. It will investigate novel connections between topological higher-rank graphs, multidimensional symbolic dynamics, cohomology theory and operator algebras. We will first study how topological graphs and their analogues can provide new and powerful visual models for the classical theory of continuous-trace C*-algebras and Fell algebras. We will build on this to develop cohomological and C*-algebraic techniques for higher-rank symbolic dynamics and to pioneer an intriguing new field of study at the nexus of three very active areas of mathematics: cohomology, symbolic dynamics and operator algebras.

Date/time Interval


  • 2012 - 2015

Sponsor Award Id


  • DP120100389

Local Award Id


  • 101489