Jeffrey Giansiracusa's talk at the 2021 annual meeting of the centre for Topological Data Analysis
Channel: 2021 annual meeting of the centre for TDA
Date: 17/09/2021

Title. Persistent homology and topological phase transitions.
Abstract. A phase transition is when a statistical system undergoes an abrupt change as a parameter such as temperature passes across a critical value. Some phase transitions are relatively easy to understand, such as the transition in the Ising model from a magnetised state to a disordered state. Some are more challenging and involve topological objects such as vortices or knots, as in the famous Berezinskii-Kosterlitz-Thouless transition in the 2D XY-model; these are called topological phase transitions. And some phase transitions are not yet understood but are expected to be topological, such as the transition in QCD (the quantum field theory that describes the strong nuclear force inside atomic nuclei) from quarks weakly interacting at high energies to confinement at low energies where we only ever see quarks bound into pairs and triples. In this talk I will report on work with Nick Sale and Biagio Lucini to use persistent homology to detect and measure properties of topological phase transitions without a priori knowledge of the details of the topological objects involved.