13.00 Dougal Davis (LSGNT): Some stacks of principal bundles over elliptic curves and their shifted symplectic geometry.
In a 2015 paper, I. Grojnowski and N. Shepherd-Barron give a recipe which produces an algebraic variety from the ingredients of an elliptic curve E, a simple algebraic group G, and an unstable principal G-bundle on E. In the case where G = D_5, E_6, E_7 or E_8, they show that a particular choice of G-bundle yields a del Pezzo surface of the same type as G. It is an open question which varieties arise for different choices of G-bundle. In this talk, I will describe how certain stacks of principal bundles on E, which are the main players in this construction, carry natural shifted symplectic and Lagrangian structures over the locus of semi-stable bundles. Time permitting, I will show how a very crude study of the degeneration of these structures at the unstable locus gives a much more direct computation of some of the canonical bundles appearing in the Grojnowski-Shepherd-Barron paper, which works for all groups and all bundles.
14.15 Francesco Meazzini (Sapienza – University of Rome): Quiver representations and Gorenstein-projective modules.
We consider a finite acyclic quiver Q and a quasi-Frobenius ring R. We then characterise Gorenstein-projective modules over the path algebra RQ in terms of the corresponding quiver representations over R, generalising the work of X.-H. Luo and P. Zhang to the case of not necessarily finitely generated RQ-modules. We recover the stable category of Gorenstein-projective RQ-modules as the homotopy category of a certain model structure on quiver representations over R.
16.00 Claudio Onorati (University of Bath): Moduli spaces of generalised Kummer varieties are not connected.
Using the recent computation of the monodromy group of irreducible holomorphic symplectic (IHS) manifolds deformation equivalent to generalised Kummer varieties, we count the number of connected components of the moduli space of both marked and polarised such manifolds. After recalling basic facts about IHS manifolds, their moduli spaces and parallel transport operators, we show how to construct a monodromy invariant which translates this problem in a combinatorial one and eventually solve this last problem.