# Clifford Structures in Noncommutative Geometry and the Standard Model of Particle Physics

## GAP Seminar

## Meeting Details

For more information about this meeting, contact Ping Xu, Nigel Higson, Mathieu Stiénon, Kendra Stauffer, Matthew Peddie.

**Speaker:** Francesco D'Andrea, University of Naples Federico II

**Abstract:** I will give a brief review of the spectral action approach to field
theory, and discuss some recent results.
On a Riemannian spin manifold M, an algebraic characterization of the
module of Dirac spinors (sections of the spinor bundle) is as the Morita
equivalence bimodule between the algebra of continuous functions on M
and the Clifford algebra bundle. In the case of Hodge-Dirac operator on
a oriented Riemannian manifold, on the other hand, the module of Hodge
spinors can be characterized as self Morita equivalence bimodule for the
Clifford algebra bundle. Both conditions admit a natural generalization
to non-commutative manifolds and dictate some constraints on the form of
the Dirac operator. I will report on a recent work with L. Dabrowski and
A. Sitarz, where we investigate such constraints for the spectral triple
of the Standard Model of elementary particles.

## Room Reservation Information

**Room Number:** 320 Whitmore

**Date:** 09/19/2017

**Time:** 2:30pm - 3:20pm