Open Problems on Central Simple Algebras

We provide a survey of past research and a list of open problems regarding central simple algebras and the Brauer group over a field, intended both for experts and for beginners.Comment: v2 has some small revisions to the text. Some items are re-numbered, compared to v

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

Essential p-dimension of the normalizer of a maximal torus

We compute the exact value of the essential p-dimension of the normalizer of a split maximal torus for most simple connected linear algebraic groups. These values give new upper bounds on the essential p-dimension of some simple groups, including some exceptional groups. For each connected simple algebraic group, we also give an upper bound on the essential p-dimension of any torus contained in that group. These results are achieved by a detailed case-by-case analysis