Research group
Geometry
Mon, 10 Nov 2014
14:15
L5

Tropical moment maps for toric log symplectic manifolds

Marco Gualtieri
(Toronto)
Abstract

I will describe a generalization of toric symplectic geometry to a new class of Poisson manifolds which are
symplectic away from a collection of hypersurfaces forming a normal crossing configuration.  Using a "tropical
moment map",  I will describe the classification of such manifolds in terms of decorated log affine polytopes,
in analogy with the Delzant classification of toric symplectic manifolds. 

Mon, 17 Nov 2014
14:15
L5

The Horn inequalities and tropical analysis

Andras Szenes
(Geneva)
Abstract

 I will report on recent work on a tropical/symplectic approach to the Horn inequalities. These describe the possible spectra of Hermitian matrices which may be obtained as the sum of two Hermitian matrices with fixed spectra. This is joint work with Anton Alekseev and Maria Podkopaeva.

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.
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