PAPERS 1. Computing the modular degree of an elliptic curve Postscript PDF 2. Resolution of class number 100 for imaginary quadratic fields Postscript PDF List of fundamental discriminants here 3. Real zeros of real odd Dirichlet L-functions Postscript PDF 4. A database of elliptic curves---first report Postscript PDF (Joint with William A. Stein) 5. Constructing elements in Shafarevich-Tate groups of modular motives PS PDF (Joint with Neil P. Dummigan and William A. Stein) 6. Rank distribution in a family of cubic twists Postscript PDF 7. Elliptic curves of large rank and small conductor Postscript PDF (Joint with Noam D. Elkies) 8. Modular Parametrizations of Neumann--Setzer Elliptic Curves Postscript PDF (Joint with William A. Stein) 9. Explicit lower bounds on the modular degree of an elliptic curve Postscript PDF 10. Some remarks on Heegner point computations Postscript PDF 11. A note on integral points on elliptic curves Postscript PDF 12. Discretisation for odd quadratic twists Postscript PDF (Joint with J. Brian Conrey, Michael O. Rubinstein, and Nina C. Snaith) 13. The power of logarithm for quadratic twists Postscript PDF (Joint with Christophe Delaunay) 14. Symmetric power L-functions of elliptic curves Postscript PDF (Joint with Phil Martin) 15. Average Ranks of Elliptic Curves External Link (Joint with Baur Bektemirov, Barry Mazur, and William Stein) 16. Some heuristics about elliptic curves Postscript PDF 17. Critical values of symmetric power $L$-functions Postscript PDF (Joint with Neil Dummigan) 18. Root numbers of symmetric powers Postscript PDF (Joint with Neil Dummigan and Phil Martin) 19. On elliptic curves and random matrix theory Postscript PDF 20. On the Extremality of an 80-Dimensional Lattice Postscript PDF (Joint with Damien Stehle) 21. Computing with Hecke Grossencharacters Postscript PDF 22. Another 80-dimensional extremal lattice PDF 23. Some comments about Indefinite LLL PDF 24. Ranks of quadratic twists of the congruent number curve PDF (With Steve Donnelly, Noam Elkies, Tom Fisher, Andrew Granville, and Nick Rogers) 25. Hypergeometric motives notes PDF Also the Magma handbook chapter PDF 26. Jacobi sum motives and Grossencharacters PDF EXPOSITORY PAPERS AND SHORT NOTES The Green-Tao Theorem Postscript PDF On Sums of Four Cubes Postscript PDF Note on the Chowla conjecture Postscript PDF Notes from a class on sieves Postscript PDF Notes from talks about the work of Connes Postscript PDF Discursus on rank 21 PDF Comments on the Deuring-Heilbronn phenomenon PDF IN PROGRESS (or reached a deadend) Isogenies of Elliptic Curves Postscript (Joint with John E. Cremona) Polynomial Families and the Davenport-Mason bound Postscript (Joint with Noam D. Elkies) Searching for points p-adically Postscript PAPERS ON COMPUTER CHESS Move similarity analysis in chess programs PDF (Joint with Don Dailey and Adam Hair) Solved openings in Losing Chess PDF Losing Chess: 1. e3 wins for White PDF Recap of the Rybka case PDF (Expository)