COLUMBIA UNIVERSITY Department of Mathematics ELLIS R. KOLCHIN MEMORIAL LECTURES   Johan de Jong Massachusetts Institute of Technology   Rational Connectivity and Moduli Spaces of Rational Curves   Abstract: We will try to introduce the audience to the geometry of moduli spaces of rational curves on algebraic varieties. There are phenomena that suggest a relation between rational connectivity, existence of rational points on varieties and the geometry of the moduli spaces of rational curves. Apart from a few general results, more detailed results have been mainly restricted to the case of hypersurfaces of low degree in projective spaces. We will try to give an impression of what is going on in this very active field. 312 Mathematics Building   Friday, April 25 4:30 p.m.   Tea will be served at 3:45 p.m. - 508 Mathematics Building   Directions to Columbia University