Cycles on the Moduli Space of Abelian Varieties

In this paper a number of results on cycles on the moduli space of principally polarized abelian varieties is presented. Results include a determination of the tautological ring, bounds on the order of torsion of the top Chern class $\lambda_g$ and a determination of the cycle classes of the Ekedahl-Oort stratification in characteristic $p$. It includes as special cases formulas for the classes of loci like the $p$-rank $\leq f$ locus or the $a$-number $\geq a$-locus. The results on the tautological ring are my own work, the results on the torsion of $\lambda_g$ and on the cycle classes of the Ekedahl-Oort stratification are joint work with Torsten Ekedahl and some of the results on curves are joint work with Carel Faber.Comment: Plain TeX, 22 pages; an erroneous lemma correcte

Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii

Discussion of ``2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization'' by V. Koltchinskii [arXiv:0708.0083]Comment: Published at http://dx.doi.org/10.1214/009053606000001073 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org