Motives and periods in Bianchi IX gravity models

In this paper we show that the heat coefficients of the Dirac-Laplacian of SU(2)-invariant Bianchi IX metrics are periods of motives of complements in affine spaces of unions of quadrics and hyperplanes

Spectral action for Bianchi type-IX cosmological models

In this paper we prove a rationality phenomena for the coefficients of the heat kernel expansion of the Dirac-Laplacian of Bianchi IX cosmological models. Due the complexities arising from the anisotropic nature of the model, we present a novel method of writing the heat coefficients as Wodzicki resiudes of certain Laplacians and then provide an elegant proof of the rationality result. That is, we show that each coefficient is described by a several variable polynomial with rational coefficients of the cosmic expansion factors and their higher derivatives of a certain order. This result confirms the arithmetic nature of the complicated terms in the expansion

QCD and strongly coupled gauge theories : challenges and perspectives

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.Peer reviewe