Research group
Geometry
Mon, 20 Oct 2014

14:15 - 16:30
L5

Mirror symmetry for varieties of general type

Mark Gross
(Cambridge)
Abstract
I will discuss joint work with Ludmil Katzarkov and Helge Ruddat. Given a hypersurface X in a toric variety of positive Kodaira dimension, (with a certain number of hypotheses) we construct an object which we believe can be viewed as the mirror of X. In particular, it exhibits the usual interchange of Hodge numbers expected in mirror symmetry. This may seem puzzling at first. For example, a curve of genus g would be expected to have a mirror such that h^{0,0}=g, which is not possible for a variety. However, our mirror is a singular scheme Y along with a perverse sheaf F, whose cohomology carries a mixed Hodge structure. It then makes sense to compute Hodge numbers for F, and we find the traditional exchange of Hodge numbers.
Mon, 19 May 2014

14:15 - 15:30
L5

Variation of the moduli space of Gieseker stable sheaves via Quiver GIT

Julius Ross (Cambridge)
Abstract

 I will discuss joint work with Daniel Greb and Matei Toma in which we introduce a notion of Gieseker-stability that depends on several polarisations.  We use this to study the change in the moduli space of Giesker semistable sheaves on manifolds giving new results in dimensions at least three, and to study the notion of Gieseker-semistability for sheaves taken with respect to an irrational Kahler class.

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