Algebraic and Symplectic Geometry Seminar

Tue, 16/10/2007
15:45
Tommaso Pacini (Oxford) Algebraic and Symplectic Geometry Seminar Add to calendar L3
The theory of Special Lagrangian (SL) submanifolds is the natural point of intersection between various classical (Lagrangian and volume-minimizing submanifolds) and contemporary (Mirror Symmetry and invariants of Calabi-Yau manifolds) topics. The key problem is how to characterize the compactified moduli space of SLs. Equivalently, to understand which SL singularities admits desingularizations. Our aim is to present some explicit examples, topological results and simple observations which shed some light on the nature and complexity of this problem, and which we expect will be a useful foundation for future progress in the field. This is joint work with M. Haskins (Imperial College), cfr. arXiv:math/0609352.
Tue, 23/10/2007
15:45
Hiroshi Iritani (Kyushu and Imperial College) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Tue, 06/11/2007
14:45
Ann-Sophie Kaloghiros (Cambridge) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Tue, 20/11/2007
14:45
Christian Pauly (Montpellier) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Tue, 27/11/2007
13:00
Olivier Schiffmann (Paris) Algebraic and Symplectic Geometry Seminar Add to calendar L1
We provide a realization of Cherednik's double affine Hecke algebras (for GL_n) as a convolution algebra of functions on moduli spaces of coherent sheaves on an elliptic curve. As an application we give a geometric construction of Macdonald polynomials as (traces of) certain natural perverse sheaves on these moduli spaces. We will discuss the possible extensions to higher (or lower !) genus curves and the relation to the Hitchin nilpotent variety. This is (partly) based on joint work with I. Burban and E. Vasserot.
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