IHP (Paris)/ ICTP (Trieste) From: "Stephen S. Kudla" To: amod@math.berkeley.edu, mantovan@math.harvard.edu, prasad@math.uchicago.edu, was@math.harvard.edu, wjm@math.umd.edu, wrmann@math.harvard.edu, trehan@math.umd.edu, snitz@math.umd.edu, fischman@math.ucla.edu, dickinso@math.harvard.edu, htwu@math.ucla.edu, debacker@math.uchicago.edu Date: Sun, 21 Jan 2001 16:10:31 -0500 Dear IHP/ICTP participant! We are currently in the process of writing up a final report on the NSF Grant which provided support for US participants in the program at the IHP in Paris last spring and the program at the ICTP in Trieste in August. Could you please send us a couple of sentences about your activities (e.g., what lecture series you attended, who you met and talked math with, what work you did there, or how participation in the program benefited your work/ expanded your horizons, etc.) This information will make our task very much easier and will hopefully encourage the NSF to fund such activites in the future! Finally, it would be helpful if you could take a moment to do this right away (rather than sending information in a rush later), since we are under some pressure to finish this chore this month. Best wishes! Steve Kudla Freydoon Shahidi ---------------- OK, here I go: What I want to say: 1) Went to many of the lectures in the automorphic forms workshop. 2) Finished a paper with Kevin Buzzard on Artin's conjecture. 3) Made significant progress towards finishing a paper with Loic Merel on torsion points on elliptic curves 4) Proved that every element of Sha is visible somewhere, following a conversation with Ralph Greenberg. 5) Formulated a tentative strategy for constructing points on elliptic curves of even analytic rank > 0 whose Shafarevich-Tate is finite. I was very productive during the month that I visited the IHP in Paris. I was stimulated by the talks on automorphic forms, which I attended regularly. Kevin Buzzard and I finished a joint paper on Artin's conjecture about icosahedral Galois representation, which was the culmination of a three-year project. Loic Merel and I had several intense discussions about torsion points on elliptic curves, and made progress that allowed us to nearly finish a joint paper. Building on a dinner conversation with Ralph Greenberg, I noticed that there is a simple proof that every element of the Shafarevich-Tate group of an abelian variety is visible somewhere, thus improving on an earlier observation of Johan de Jong. I also formulated a tentative strategy for constructing points on elliptic curves of analytic rank > 0 whose Shafarevich-Tate group is finite. I described this strategy in an Utrecht talk in honor of Franz Oort, which I delivered immediately after my stay in Paris.