Sage Days 5 Schedule

SUNDAY ======

MORNING TALK 1 Speaker: William Stein (or Barry Mazur?) Title: On convergence in the Sato-Tate conjecture

MORNING TALK 2 Speaker: David Roe Title: p-adic Arithmetic in SAGE

AFTERNOON TALK Speaker: Fernando Rodriguez-Villegas Title: [something about identities between p-adic multipolylogs and p- adic zeta values]

After the afternoon talk today we will have an organisational meeting to discuss the plan for working groups for the remainder of the workshop.

EVENING TALK Speaker: William Stein and/or Robert Bradshaw Title: Algebraic Number Theory in SAGE, a Status Report

Speaker: Craig Citro Title: Modular forms in SAGE: A status report

MONDAY ======

MORNING TALK 1 Speaker: Amnon Besser Title: On the Computation of p-adic Height Pairings on Jacobians of Hyperelliptic Curves

MORNING TALK 2 Speaker: Robert Bradshaw Title: Coleman integration

AFTERNOON TALK Speaker: Martin Albrecht Title: Commutative Algebra in SAGE

EVENING TALK Speaker: Bill Hart Title: FLINT status report

TUESDAY =======

MORNING TALK 1 Speaker: Gonzalo Tornaria Title: [something about stark-heegner points and shimura correspondence]

MORNING TALK 2 Speaker: Dimitar Jetchev Title: [something about explicit Heegner points]

AFTERNOON TALK Speaker: Michael Abshoff Title: CoCoALib

EVENING TALK Speaker: Robert Bradshaw Title: Cython status report

WEDNESDAY =========

MORNING TALK 1 Speaker: J-P. Serre Location: Science Center 507 Title: Finite Groups in Number Theory (part 3)

MORNING TALK 2 Speaker: William Stein Title: Computing p-adic Invariants of Elliptic Curves and Applications of Iwasawa theory to BSD

AFTERNOON TALK Speaker: Robert Bradshaw Title: Coercion Status Report

EVENING TALK (can we really have a talk now? probably this will get moved to a previous day?) Speaker: Michael Abshoff Title: Using trac to manage SAGE development workflow

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Possible talks:

[technical math] Speaker: Amnon Besser Title: On the Computation of p-adic Height Pairings on Jacobians of hyperelliptic Curves Abstract: The talk will present an algorithm for the computation of p-adic height pairings on hyperelliptic curves over number fields. Our work is not directly related to the work of Mazur Stein and Tate, though there are some similarities in the difficulties that occur and in the use of Kedlaya's algorithm. I will first explain where this height pairing arise, and how it decomposes into a sum of local terms at the places of the field. The most interesting is for places above the prime p. We use a description of these local terms given by Coleman and Gross that uses the theory of Coleman integration. There are two parts for the computation at these primes. One computes a certain projection from the space of meromorphic forms on the curve to its first de Rham cohomology, which can be computed using Coleman integration and the theory of the so called double index. The second involves computation of Coleman integrals, which are however mroe general than the ones computed in recent work o! n the subject (Gutnik, Kedlaya, ...) so there are some tricks involved which I'll explain. Finally I will discuss the situation at other primes, where there are still some delicate issues to resolve.

[general computer] Speaker: Craig Citro Title: Modular forms in SAGE: A status report Abstract: I'll give a short overview of the state of affairs of modular forms in SAGE. Mostly, I'll detail what we can do, what MAGMA can do that we can't, and some speed comparisons.

[technical computer] Speaker: Robert Bradshaw. - Cython Status Report

[general/technical computer] Speaker: Robert Bradshaw. - Coercion Status Report (maybe a bit more of a status report, I intend to talk about the "right" way to discover coercion and why the idea of base extension is wrong.)

[technical math] Speaker: Robert Bradshaw. - Coleman integration: I'm sure that Kiran Kedlaya would have more to say about this than me--I'll be in touch with him about this.

[technical math] Speaker: Gonzalo T. "PS: I was considering offering a talk on my work with darmon (stark-heegner points and shimura correspondence) but I still need a few hours to make a concrete proposal. Do you think this might be interesting for the program? "

[technical math] Speaker: Fernando Rodriguez-Villegas: " If there's a free slot I wouldn't mind talking about some work in progress which involves identities between p-adic multipolylogs and p-adic zeta values. Some I can (almost) prove others I can't and I find pretty surprising. Mostly I'd like to have some feedback on it. It wouldn't really be that computational except for the issue of how to compute linear relations among constants in the p-adics (but the again may be this is well known--to others).

Noam: I thought this basically comes down to lattice basis reduction, much like linear relations among real numbers (or even vectors in R^n). Since gp's algdep() program has no problem recognizing p-adic numbers as algebraic I imagine that this is not just "known" but already implemented, at least in gp and for this special case. Or is there some specific context here that requires going beyond the usual lattice method?

[technical math] Speaker: W Stein p-adic BSD (joint with Wuthrich) "TITLE: Computing p-adic Invariants of Elliptic Curves and Applications of Iwasawa theory to BSD (the talk C. Wuthrich would have given if he could attend the workshop, but I could give, since it's a joint project between me and him -- in fact, I'd use his slides -- he gave the talk at a conference in England yesterday). "

[general math] Speaker: W Stein or ?? TITLE: On convergence in the Sato-Tate conjecture (application of Sage to studying how quickly convergence happens in Sato-Tate; leads to conjecture; joint with Mazur). (by me and or Barry Mazur)

[technical math] Speaker: Dimitar Jetchev "I can give my talk from UW on Explicit Heegner points. The title and the abstract are exactly the same! "

[general computer] Speaker: Bill Hart " TITLE: FLINT status report - fast library for number > theory > (by Bill Hart) I can give a *short* talk. There are a couple of interesting things to say, however there will probably be more to say by SAGE days 6. " "A short talk on short division : FLINT (Fast Library for Number Theory) a status report by Bill Hart. FLINT is a C library, in the very early stages of development, which has the aim of extending the state of the art in core arithmetic computations and eventually algebraic number theory. We will briefly discuss progress that has been made so far in polynomial and integer arithmetic, including a new variant/implementation of Mulder's recursive polynomial "short division" algorithm which we have worked up for doing faster polynomial division. "

[general computing/math] Speaker: David Roe "p-adics" " Speaker: Title: Status Report on p-Adic Arithmetic in Sage David Roe I will outline the current status of p-adic arithmetic in Sage. In particular, I will discuss the different types of p-adics in Sage, extensions of Qp, polynomials and matrices over such local fields and their rings of integers. I will outline a number of algorithms for treating precision in polynomial and matrix computations. Come with comments on what aspects of p-adic arithmetic are most needed for your own projects. "

[general computing] Speaker: William Stein > TITLE: Algebraic Number Theory in Sage, a Status Report > (by me and/or Robert Bradshaw)

[general computing] Speaker: M Abshoff > TITLE: Using trac to manage Sage development workflow > (by Michael Abshoff)

[general computing] Speaker: M Abshoff " TITLE: [Ap]CocoaLib

[general computing] Speaker: M Albrecht "> Commutative Algebra in SAGE > I will cover libSINGULAR (with some examples, to show that the code isn't > as scary as people believe), a bit of PolyBoRi, maybe something about > CoCoALib, some benchmarks, and stuff we desperately need and don't know how > to get. Obviously, I would throw in some benchmarks and stuff. Actually, I would like to add some (unrelated) slides on the state of sparse linear algebra over finite fields. That would cover what package can do it (not many!) and how SAGE is in that area (surprisingly good it seems for now) and what is done to improve it. Also, someone in the audience might have some input on William's echelon via solve idea adapted to this setting. "