Past Algebraic and Symplectic Geometry Seminar

1 December 2009
15:00
Simon Donaldson
Abstract
This talk will be largely speculative. First we consider the formal properties that could be expected of a "topological field theory" in 6+1 dimensions defined by $G_2$ instantons. We explain that this could lead to holomorphic bundles over moduli spaces of Calabi-Yau 3-folds whose ranks are the DT-invariants. We also discuss in more detail the compactness problem for $G_2$ instantons and associative submanifolds. The talk will be held in Room 408, Imperial College Maths Department, Huxley Building, 180 Queen’s Gate, London.
  • Algebraic and Symplectic Geometry Seminar
1 December 2009
13:30
Simon Donaldson
Abstract
This talk will review material, well-known to specialists, on calibrated geometry and Yang-Mills theory over manifolds with holonomy $SU(3)$, $G_2$ or $Spin(7)$. We will also describe extensions of the standard set-up, modelled on Gromov's "taming forms" for almost-complex structures. The talk will be held in Room 408, Imperial College Maths Department, Huxley Building, 180 Queen’s Gate, London.
  • Algebraic and Symplectic Geometry Seminar
24 November 2009
15:45
Julius Ross
Abstract
There is a conjectural relationship due to Yau-Tian-Donaldson between stability of projective manifolds and the existence of canonical Kahler metrics (e.g. Kahler-Einstein metrics). Embedding the projective manifold in a large projective space gives, on one hand, a Geometric Invariant Theory stability problem (by changing coordinates on the projective space) and, on the other, a notion of balanced metric which can be used to approximate the canonical Kahler metric in question. I shall discuss joint work with Richard Thomas that extends this framework to orbifolds with cyclic quotient singularities using embeddings in weighted projective space, and examples that show how several obstructions to constant scalar curvature orbifold metrics can be interpreted in terms of stability.
  • Algebraic and Symplectic Geometry Seminar
10 November 2009
15:45
Christian Pauly
Abstract
In this talk I will introduce and study opers over a smooth projective curve X defined over a field of positive characteristic. I will describe a bijective correspondence between the set of stable vector bundles E over X such that the pull-back F^*(E) under the Frobenius map F of X has maximal Harder-Narasimhan polygon and the set of opers having zero p-curvature. These sets turn out to be finite, which allows us to derive dimensions of certain Quot-schemes and certain loci of stable Frobenius-destabilized vector bundles over X.
  • Algebraic and Symplectic Geometry Seminar
20 October 2009
15:45
Balazs Szendroi
Abstract
I will talk about joint work with Dimca, respectively Behrend and Bryan, in which we refine the numerical DT-Behrend invariants of Hilbert schemes of threefolds by using vanishing cycle motives (a la Kontsevich-Soibelman) or mixed Hodge modules, leading to deformed MacMahon formulae.
  • Algebraic and Symplectic Geometry Seminar
20 October 2009
14:00
Balazs Szendroi
Abstract
I will talk about joint work with Dimca, respectively Behrend and Bryan, in which we refine the numerical DT-Behrend invariants of Hilbert schemes of threefolds by using vanishing cycle motives (a la Kontsevich-Soibelman) or mixed Hodge modules, leading to deformed MacMahon formulae.
  • Algebraic and Symplectic Geometry Seminar

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