Public Lectures

FRIDAY, October 6, 2006 at 4:00 pm

Koszul divisors on moduli space of curves

Gabril Farkas


SATURDAY, October 7, 2006 at 2:30 pm

Intersection pairings in singular moduli spaces of bundles

Lisa Jeffrey

Joint work with Kiem, Kirwan and Woolf (math.SG/0505362, published in the most recent issue of Transformation Groups). We describe intersection pairings on the cohomology of the moduli space M(n,d) of holomorphic bundles of rank n and degree d when n and d are not coprime, so the space M(n,d) is in general singular. We treat the intersection cohomology of M(n,d) and the ordinary cohomology of a partial resolution of singularities {\widetilde M}(n,d). We pay particular attention to the case M(2,0). We remark that although intersection cohomology does not in general have a ring structure, it is equipped with a pairing between classes of complementary dimensions.


SATURDAY, October 7, 2006 at 4:00 pm

Integral constraints on hyperkahler monodromy operators

Eyal Markman

We will review the role monodromy groups play in the formulation of Torelli questions. The Torelli Theorem for K3 surfaces states, that their isomorphism class is determined by their weight 2 integral Hodge structure. An analogous Torelli question was formulated for higher dimensional hyperkahler varieties, again in terms of their weight 2 Hodge structure. In the latter case, the second cohomology does not generate the cohomology ring.
We use equivalences of derived categories, in order to calculate the monodromy group of Hilbert schemes of n points on a K3 surface. The computation shows, that the above statement of the Torelli conjecture is wrong, and the integral Hodge structure of weight 4 contains information not encoded in weight 2. Furthermore, the information about the integral Hodge structures of all weights is encoded in the weight 4 one, although the second and fourth cohomologies still do not generate the cohomology ring if n>3.


SUNDAY, October 8, 2006 at 2:30 pm

Langlands duality on moduli spaces of Higgs bundles

Michael Thaddeus


SUNDAY, October 8, 2006 at 4:00 pm

Moduli of coherent systems on algebraic curves

Peter Newstead

Coherent systems on algebraic curves are a natural generalisation of classical linear systems. They relate to maps into Grassmannians in much the same way as linear systems relate to maps into projective spaces. As a result, they tell us something about the projective geometry of curves. However the structure of the moduli spaces which classify coherent systems is far from being completely understood. In this talk, I will give an introduction to the subject, survey results from the past 15 years and state some open problems.


MONDAY, October 9, 2006 at 2:30 pm

GV-sheaves, Fourier-Mukai transform, and generic vanishing

Minhea Popa


MONDAY, October 9, 2006 at 4:00 pm

Stable Pairs for K3 Surfaces

Aaron Bertram


Public lectures