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