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Seminars (MOSW06)

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Event When Speaker Title Presentation Material
MOSW06 5th May 2011
11:00 to 12:00
Moduli in derived categories
Classical moduli theory was born with a focus on objects we can easily see: varieties, vector bundles, morphisms, etc. In the last half-century, we have come to perceive a slew of subtler invariants, such as the derived category of coherent sheaves on a variety, that are decidedly murkier. Within the last decade, moduli spaces of objects in the derived category began to appear, drawing inspiration from birational geometry and mathematical physics. It turns out that a systematic approach to constructing these moduli spaces bears fruit in such disparate areas as Gromov-Witten theory, arithmetic geometry, and non-commutative algebra. I will describe some aspects of these moduli problems and a few of their principal applications.
MOSW06 5th May 2011
13:45 to 14:45
Moduli of sheaves and strange duality
Strange duality is a symmetry that spaces of sections of determinant line bundles over moduli spaces of sheaves are conjectured to obey. I will discuss the conjecture for moduli spaces of sheaves on K3 surfaces. Questions about the geometry of the moduli space of polarized K3s also arise.
MOSW06 5th May 2011
15:15 to 16:15
Y Toda Curve counting invariants on Calabi-Yau 3-folds
I give an introduction of Donaldson-Thomas type curve counting invariants on Calabi-Yau 3-folds, and explain the recent developments.
MOSW06 5th May 2011
16:30 to 17:30
Moduli space of bundles and Kloosterman sums
The relation between analytic properties of modular forms and arithmetic results has led to many famous results and conjectures. In the geometric analogue of this conjectural relation - called geometric Langlands correspondence quotients of the upper half plane are replaced by moduli spaces of bundles on the curve. We will try to motivate this analogy. Since the geometry of these spaces is complicated in general, very few explicit examples of such modular forms are known. In joint work with B.C. Ngô and Z. Yun - which was motivated by work of Gross and Frenkel - we found an explicit series of such forms which turn out to be closely related to classical Kloosterman sums. This gives an example of the (wild) geometric Langlands correspondence.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons