Talk by Daniel Parra
On May 4th, 2023, Daniel Parra (University of Santiago, Chile) gave a talk about "Continuum limit for a discrete Hodge-Dirac operator on square lattices" as part of the online workshop on "Dirac equation between discrete and continuous: new trends and applications" organized by Ginestra Bianconi (Queen Mary University of London) and Delio Mugnolo (FernUniversität in Hagen). This lecture is partially supported by the COST action Mathematical models for interacting dynamics on networks.
Abstract
Show Abstract
We study the continuum limit for Dirac-Hodge operators defined on the n dimensional square lattice hZ^n as h goes to 0. This result extends to a first order discrete differential operator the known convergence of discrete Schrödinger operators to their continuous counterpart. To be able to define such a discrete analog, we start by defining an alternative framework for a higher–dimensional discrete differential calculus to the standard one defined on simplicial complexes. We then express our operator as a differential operator acting on discrete forms to finally be able to show the limit to the continuous Dirac-Hodge operator.
