1IHP (Paris)/ ICTP (Trieste)
2From: "Stephen S. Kudla" <[email protected]>
3To: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]
4Date: Sun, 21 Jan 2001 16:10:31 -0500
7Dear IHP/ICTP participant!
9 We are currently in the process of writing up a final
10report on the NSF Grant which provided support for US
11participants in the program at the IHP in Paris last spring and the
12program at the ICTP in Trieste in August. Could you please send us a
13couple of sentences about your activities (e.g., what
14lecture series you attended, who you met and talked math with, what
15work you did there, or how participation in the program benefited your
16work/ expanded your horizons, etc.) This information will make our task
17very much easier and will hopefully encourage the NSF
18to fund such activites in the future!
20 Finally, it would be helpful if
21you could take a moment to do this right away
22(rather than sending information in a rush later), since
23we are under some pressure to finish this chore this month.
25 Best wishes!
27 Steve Kudla
28 Freydoon Shahidi
32OK, here I go:
34What I want to say:
351) Went to many of the lectures in the automorphic forms workshop.
362) Finished a paper with Kevin Buzzard on Artin's conjecture.
373) Made significant progress towards finishing a paper with
38 Loic Merel on torsion points on elliptic curves
394) Proved that every element of Sha is visible somewhere, following
40 a conversation with Ralph Greenberg.
415) Formulated a tentative strategy for constructing points on
42 elliptic curves of even analytic rank > 0 whose Shafarevich-Tate
43 is finite.
46I was very productive during the month that I visited the IHP in
47Paris. I was stimulated by the talks on automorphic forms, which I
48attended regularly. Kevin Buzzard and I finished a joint paper on
49Artin's conjecture about icosahedral Galois representation, which was
50the culmination of a three-year project. Loic Merel and I had several
51intense discussions about torsion points on elliptic curves, and made
52progress that allowed us to nearly finish a joint paper. Building on
53a dinner conversation with Ralph Greenberg, I noticed that there is a
54simple proof that every element of the Shafarevich-Tate group of an
55abelian variety is visible somewhere, thus improving on an earlier
56observation of Johan de Jong. I also formulated a tentative strategy
57for constructing points on elliptic curves of analytic rank > 0 whose
58Shafarevich-Tate group is finite. I described this strategy in an
59Utrecht talk in honor of Franz Oort, which I delivered immediately
60after my stay in Paris.