Open de Rham spaces refer to certain moduli spaces of meromorphic connections on the projective line. I will discuss certain aspects of these, namely their relation to quiver varieties, the existence of hyperkaehler metrics, and the computation of their E-polynomials.

One knows that any compact riemann surface of genus > 2 carries a riemanniann metric of constant curvature. In higher dimension even the existence of compact manifolds of constant negative curvature is by no means that abundant. In this lecture we will show how arithmetic enables us to construct such manifolds in every dimension greater than equal to 2.

We shall continue the discussion on the results of Marina Ratner on unipotent flows, and the techniques involved.

We shall continue the discussion on the results of Marina Ratner on unipotent flows, and the techniques involved.

We shall discuss a new method of computing (integral) homotopy groups of certain manifolds in terms of the homotopy groups of spheres. The techniques used in this computation also yield formulae for homotopy groups of connected sums of sphere products and CW complexes of a similar type. In all the families of spaces considered here, we verify a conjecture of J. C. Moore. This is joint work with Somnath Basu.

We shall discuss the results of Marina Ratner on unipotent flows, and the techniques involved.

This will be a continuation of the overview from the last week. Some details will be briefly recalled from the last time, for continuity and the benefit of new audience if any.

In a land-mark paper in 1956, J. Milnor showed that there are non standard differential structures on the 7-dimensional sphere. Six years later along with Kervaire, he introduced an abelian group structure on the set of equivalence classes of smooth structures on spheres of all dimension and determined these groups in several cases. We shall present some of the salient features of this work. This is the second talk on this topic.

This will be a continuation of the overview from the last week. Some details will be briefly recalled from the last time, for continuity and the benefit of new audience if any.