Abstracts for Seminar on Algebra, Geometry and Physics

Singular curves over number fields have properties very different from those of smooth curves:
such a curve can have the trivial Brauer group, contain infinitely many adelic points, but only
finitely many rational points or none at all. Nevertheless, finite descent explains all counterexamples
to the Hasse principle on singular curves provided all the geometric irreducible components are rational.
Singular curves can be used to construct surfaces which are counterexamples to the Hasse

To each unital C*-algebra, we associate a generalised Gelfand
spectrum in the form of the spectral presheaf. It is shown that this
assignment is contravariantly functorial, generalising the Gelfand
spectrum functor to nonabelian unital C*-algebras. We show that the
spectral presheaf is 'locally dual' to the Bohrification of a C*-algebra
in the sense of Heunen, Landsman and Spitters. Moreover, it is
demonstrated that the spectral presheaf determines the C*-algebra up to
Jordan isomorphisms in many cases, and that time evolution of a quantum

We consider a class of non-linear PDE systems, whose equations possess Noether identities (the equations are redundant), including non-variational systems (not coming from Lagrangian field theories), where Noether identities and infinitesimal gauge transformations need not be in bijection. We also include theories with higher stage Noether identities, known as higher gauge theories (if they are variational).

I will give a fairly high level introduction to topological modular forms (Tmf) and their relationship to the Witten genus. Tmf was constructed, in part, as the target of a cohomological lift of Witten genus. The Witten genus assigns a modular form to a string manifold and this assignment is invariant under string bordism. This is analogous to the A-hat genus which assigns to a spin manifold an elliptic operator which, in turn, defines a formal difference of vector spaces. Moreover the A-hat genus is invariant under spin bordism.