Student Research Projects
If you're a student at UW that intensely loves mathematics and wants to attack unsolved problems (i.e., do research) in number theory, please contact me (wstein@gmail.com).
Current Students
All students listed below are at University of Washington, unless otherwise noted.
- Jennifer Balakrishnan (Ph.D. student at MIT):
- Rigorous computation with complex-analytic L-functions (building on work of Dokchitser).
- Tom Boothby (graduate student):
- Computing L functions to high precision
- Multiplication of matrices over GF(3^k)
- Fast polynomial evaluation
- Robert Bradshaw (Ph.D. student)
- 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 (http://www.cython.org)
- Asymptotically fast exact linear algebra
- Dimitar Jetchev (Ph.D. student, 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
for higher degree newforms
- Robert Miller (Ph.D. student)
- Construction of rational points on high-rank elliptic curves using congruences and Galois cohomology
- Computation of canonical labelings of graphs
- Bobby Moretti (undergraduate):
- Weierstrass equations for elliptic curves [mostly done]
- Very high-precision evaluation of L-series of elliptic curves of high rank
- 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