Contents Preface Schedule of talks Results of Cohen-Lenstra type for quadratic function fields JEFFREY D 0 ACUTER The hardness of computing an eigenform ERIC BACH and DENIS CHARLES Constructing elliptic curves of prime order REINIER BROKER and PETER STEVENHAGEN Space-time codes and non-associative division algebras arising from elliptic curves ABDULAZIZ DEAJIM and DAVID GRANT Points of low height on JP1 over number fields and bounds for torsion in class groups ix xi 1 9 17 29 JORDAN So ELLENBERG 45 Supersingular genus-2 curves over fields of characteristic 3 EVERETT W o HOWE 49 Search techniques for root-unitary polynomials KIRAN So KEDLAYA 71 Yet more elements in the Shafarevich-Tate group of the jacobian of a Fermat Curve BENJAMIN LEVITT and WILLIAM McCALLUM 83 Stable reduction of Xo(81) KEN McMURDY 91 Isomorphism types of commutative algebras of finite rank over an algebraically closed field BJORN POONEN A short guide top-torsion of abelian varieties in characteristic p RACHEL PRIES vii 111 121
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