T. Ekholm: Contact homology of Legendrian submanifolds of standard contact R^{2n+1}. We define contact homology of Legendrian submanifolds in R^{2n+1} and use it to give new examples and new constructions of Legendrian knotted submanifolds. ----------------------------------------------------------------------- H.J. Geiges: Contact topology of torus bundles This talk discusses various aspects of the contact topology of torus bundles, such as questions of symplectic fillability and homotopy information about the space of contact structures. ----------------------------------------------------------------------- S. Strle: Homology lens spaces and four-ball I will discuss an application of Heegaard Floer homology to four-ball genus of links. The idea is to encode the information about the slice surface in a 4-manifold X, and the information about the link in its boundary Y. Using the correction term (which is analogous to Froyshov invariant in Seiberg-Witten theory) one can find obstructions to Y bounding X. This is joint work with Brendan Owens. ------------------------------------------------------------------------ D.T. Martinez: Ample bundles for odd dimensional manifolds We show how certain geometric structures on odd dimensional manifolds $M$ (analogs of symplectic structures with include contact structures, cosympletic structures, smooth taut foliations,...) give rise to ample bundles $L\rightarrow M$, out of which we produce differential topologic constructions compatible with the geometric structure. ------------------------------------------------------------------------- C. Manolescu: Gauge theory and stable homotopy We survey recent work on an algebraic-topologic approach to Seiberg-Witten theory in three and four dimensions. In dimension 4, there is a stable homotopy version of the Seiberg-Witten invariant, due to Bauer and Furuta. The basic idea is to approximate infinite-dimensional configuration spaces by finite-dimensional ones. Doing the same thing in dimension 3, one can construct a spectrum whose homology is the Floer homology, as well as define relative invariants of four-manifolds with boundary. The end result is expected to be a "spectra-valued topological quantum field theory." ----------------------------------------------------------------------- A. Teleman: Applications of gauge theory in complex geometry We present several interesting applications of Gauge Theory in Complex Geometry. First, we will present a short proof of Bogomolov's theorem on class VII surfaces with $b_2=0$, which uses Donaldson theory. Second, we will explain how Donaldson Theory and the Witten conjecture can be used to solve the existence problems for holomorphic structures on vector bundles over non-algebraic surfaces. Third, we describe the "gauge theoretical' Gromov-Witten invariants of the Grassmann manifold, and show how these invariants can be used to solve an enumerative problem in Algebraic Geometry. ---------------------------------------------------------------------------- M. Abreu: Topological decomposition of a symplectomorphism group Let M denote the manifold S^2 x S^2 equipped with a symplectic form having ratio of the area of the two spheres in the interval (1,2]. In this talk I will describe recent work of S.Anjos and G.Granja, expressing the symplectomorphism group of M as the pushout (or amalgam) of some of its compact Lie subgroups. This result suggests an appropriate framework to derive and interpret previous results regarding the topology of certain symplectomorphism groups. ----------------------------------------------------------------------- P. Ghiggini: Classification of tight contact structures on some Seifert manifolds We give a complete isotopy classification of tight contact structures on Seifert manifolds over $T^2$ with one singular fibre. -----------------------------------------------------------------------