RECENT PROGRESS IN TWISTED REAL STRUCTURES FOR SPECTRAL TRIPLES

Within the approach to NCG based on Connes' spectral triples, real spectral triples, where the addition of a so-called real structure allows the differentiation between spin^c and spin structures and refines the K-homology, are of particular interest. Twisted real structures are a generalisation of these real structures. In this talk, I will give an introduction to real structures, and explain the motivation for 'twisting' them coming from noncommutative conformal rescalings, along with reviewing recent work in this direction. I will then focus on some new applications to Riemannian manifolds and spectral gauge theory on almost-commutative spaces as well as connections to twisted spectral triples. In this vein, I will then touch on ongoing work including applications of twisted real structures to twisted spectral triples.