ar X iv : m at h / 06 10 30 1 v 1 [ m at h . A G ] 9 O ct 2 00 6 ALGEBRAIC NAHM TRANSFORM FOR PARABOLIC HIGGS BUNDLES ON P

ar X iv : m at h / 06 07 06 1 v 2 [ m at h . A G ] 1 7 N ov 2 00 7 POISSON GEOMETRY OF PARABOLIC BUNDLES ON ELLIPTIC CURVES

The moduli space of G-bundles on an elliptic curve with additional flag structure admits a Poisson structure. The bivector can be defined using double loop group, loop group and sheaf cohomology constructions. We investigate the links between these methods and for the case SL2 perform explicit computations, describing the bracket and its leaves in detail.

ar X iv : d g - ga / 9 51 00 06 v 1 2 3 O ct 1 99 5 GROUP SYSTEMS , GROUPOIDS , AND MODULI SPACES OF PARABOLIC BUNDLES

ar X iv : m at h / 06 06 65 4 v 2 [ m at h . A T ] 1 6 O ct 2 00 6 EULER CHARACTERISTICS OF ALGEBRAIC VARIETIES

The aim of this note is to study the behavior of intersection homology Euler characteristic under morphisms of algebraic varieties. The main result is a direct application of the BBDG decomposition theorem. Similar formulae for Hodge-theoretic invariants of algebraic varieties were announced by the first and third authors in [4, 11].

ar X iv : m at h / 06 09 42 6 v 3 [ m at h . C O ] 1 5 O ct 2 00 6 SUM - PRODUCT ESTIMATES IN FINITE FIELDS VIA KLOOSTERMAN

We establish improved sum-product bounds in finite fields using incidence theorems based on bounds for classical Kloosterman and related sums.

ar X iv : m at h / 06 10 50 1 v 2 [ m at h . G T ] 1 8 O ct 2 00 6 INTRINSIC LINKING IS ARBITRARILY COMPLEX

We prove that given any n, λ ∈ N, there is a graph G which has the property that every embedding of G in R contains an ncomponent link all of whose components are pairwise linked with linking number greater than λ.