Papers I can finish and publish without major difficulty: [ ] Calegari-Stein: Non-eisenstein descent - numerous small technical questions to answer, still - most of it should now be do-able in Sage; patch up anything that isn't [ ] Stein: Computing End(A_f) and minimal degree of A_f^ --> A_f. - the thing that I did with Tseno - polish and publish - more data should be computable these days - I'm not sure the algorithm is even implemented in Sage, but it shouldn't be too hard [ ] Kamienny-Stein-Stoll: Quartic torsion points - easy approach: just let it depend on Magma. Lame. Or just put the Magma part in a separate paper not by me (use a pseudonym or just Stoll). - harder: determine cupsidal torsion subgroup using new ideas; at least helps - hard as hell: implement Hesse's algorithm in Sage for this (this is what I want to do -- it's weak to apply Hesse to solve this problem, if I don't truly understand it, anyways.) - Do a better writeup of the intro based on talks I've given [X] Stein: Kolyvagin's conjecture - first ever verification of it - interesting theoretical results about kolyvagin derivative: highlight in intro - just needs polish, at this point. Maybe improve algorithm and redo tables, better. - Should add more about what is in Stein-Weinstein [ ] Stein-Weinstein: Kolyvagin densities - explains data from Kolyvagin conj - need tex file - just needs polish, I think. Jared wants to push the results too far, maybe? [ ] Stein-Wuthrich: Aplying p-adic methods to bound Shafarevich-Tate groups - need to apply it to get some big interesting tables/computational results, or what is the point!? - there is a weird merge issue regarding reducible case [ ] Bradshaw-Stein: Provable computation of motivic L-functions - put his thesis into a paper, and give it my spin and numerical data - motivate with quote from Dokchitser's paper; once this paper is published, people will be able to reference it when claiming the existence of algorithms to do blah, blah, even if they don't actually _use_ it as such. - just a part of the thesis! [X] Bardshaw-Stein: A conjectural Kolyvagin-style bound over ring class fields for curves with analytic rank at least 2. - Based on Robert's calculations in his thesis - Very easy sell to publish this in a good journal - Can be viewed as a sort of follow up to a Bertolini-Darmon paper More speculative papers: [ ] Computation the exact rational torsion subgroup of J0(N), J1(N) and A_f - Uses idea of Mazur and Merel, if it works. - Could lead to some interesting conjectures and/or theorems. - Probably useful data for quartic torsion project [ ] A Database of Elliptic Curves over Q(sqrt(5)) - Could have many co-authors (e.g., Aly, Joanna, Elkies, Voight, Dembele, ...)? Unclear. - Potential contents: - fairly complete data - explain algorithms, e.g., how to make Dembele's Q(sqrt(5)) paper actually *really* fast - linear algebra to go from Dembele's paper to actually enumerating rational eigenforms - Statistics about resulting data - Generalization of Stein-Watkins method for enumerating curves - How to compute analytic ranks - Full/partial BSD verification in some cases - Summary of known results about curves over Q(sqrt(5)) Books I'm working on finishing up: [ ] Mazur-Stein: A popular book on the Riemann-Hypothesis - Tricky because of theoretical issues with non-tempered disributions, which we're confronted with. [ ] Ribet-Stein: Lectures on Modular Forms and Hecke operators - Just needs polish and more examples. - Did get some good polish when I taught out of it in 2003