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Author: William A. Stein
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Student Research

See my research blog for project ideas.

Current Students (who I mentor)

All students listed below are at University of Washington, unless otherwise noted.

  • Alyson Deines (Ph.D. student):
    • Kolyvagin's conjecture over totally real fields
  • Joanna Gaski (Masters thesis student)

Recent Students (who I played a nontrivial role mentoring)

  • Robert Bradshaw (Ph.D. student, expected Ph.D. 2010):
    • Thesis: Computing L-functions
    • Rigorous computation with complex-analytic L-functions (building on work of Dokchitser).
    • Explicit investigations into p-adic analogues of the Birch and Swinnerton-Dyer conjecture for jacobians of genus 2 curves
    • Coleman integration
    • p-adic heights and Monsky-Washnitzer cohomology
    • Symbolic algebra (automatic coercion)
    • Compilers (

    • Asymptotically fast exact linear algebra
  • Robert Miller (Ph.D. student, expected Ph.D. 2010):
    • Thesis: Computational Verification of the Birch and Swinnerton-Dyer Conjecture
    • Construction of rational points on high-rank elliptic curves using congruences and Galois cohomology
    • Computation of canonical labelings of graphs
  • Tom Boothby (Masters student):
    • Computing L-functions to high precision
    • Multiplication of matrices over GF(3^k)
    • Fast polynomial evaluation
    • Tables of modular forms
  • Jennifer Balakrishnan (Ph.D. student at MIT):
    • Explicit computation of Kolyvagin classes
  • Christopher Swierczewski (undergraduate):
    • Senior Thesis on the relationships between the Convergence Sato-Tate Conjecture and the Generalized Riemann Hypothesis. In particular, a focus on the implication of the latter conjecture from the former. Examining different formulations of Sato-Tate.
    • Computations related to the Sato-Tate conjecture
  • Bobby Moretti (undergraduate):
  • Dimitar Jetchev (Ph.D., Berkeley)
    • Ph.D. thesis improving on Kolyvagin's Sha bounds
    • Explicit computation of Heegner points and Kolyvagin classes
  • Emily Kirkman (undergraduate)
    • Senior thesis
  • Koopa Koo (Ph.D. student of Greenberg, UW)
    • Irreducibility of Hecke polynomials
    • $a_p \in \mathbf{Z}$ for higher degree newforms

  • Ifti Burhanuddin (Ph.D, USC, 2007)
    • Thesis: "Some computational problems motivated by the Birch and Swinnerton-Dyer Conjecture"

2013-05-11 18:34