Oxford

Anthony Lock will speak on "A Column Model of Moist Convection".

A parabolic bundle on a marked curve is a vector bundle with extra structure (a flag) in each of the fibres over the marked points, together with data corresponding to a choice of stability condition Parabolic bundles are natural generalisations of vector bundles when the base comes with a marking (for example, they partially generalise the Narasimhan-Seshadri correspondence between representations of the fundamental group and semistable vector bundles), but they also play an important role in the study of pure sheaves on nodal curves (which are needed to compactify moduli of vector bundles on stable curves). Consider the following moduli problem: pairs $(C,E)$ of smooth marked curves $C$

and semistable parabolic bundles $E\rightarrow C$. I will sketch a construction of projective moduli spaces which compactify the above moduli problem over the space of stable curves. I'll discuss further questions of interest, including strategies for understanding the cohomology of these moduli spaces, generalisations of the construction to higher-dimensional base schemes, and possible connections with Torelli theorems for parabolic vector bundles on marked curves.