Differences between revisions 18 and 66 (spanning 48 versions)

Sage Days 5 Schedule

The times are as follows, unless otherwise stated below.

MORNING TALK 1 (9:15 - 10:15)
MORNING TALK 2 (10:30 - 11:30)
AFTERNOON TALK (1-2pm)
DINNER (5-7pm)
EVENING REPORTS (7-8pm)
EVENING WORKING SESSION (8pm-?)

SATURDAY

7pm -- Dinner at Penang in Harvard Square; 57 JFK Street, Harvard Square, Cambridge, MA 02138. We would like to make a reservation; please let William know if you plan to attend.

SUNDAY

MORNING TALK 1 (9:15-10:15)

Speaker: William Stein
Title: Computations Related to the Birch and Swinnerton-Dyer Conjecture using Sage

Slides Google Video

MORNING TALK 2 (10:30-11:30)

Speaker: David Roe
Title: p-adic Arithmetic in SAGE

Abstract: 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 \mathbf Q_p, 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.

Slides Google Video part 1 (of 2) Google Video part 2 (of 2)

AFTERNOON TALK (1-2)

Speaker: Fernando Rodriguez-Villegas
Title: Identities between p-adic multi-polylogs and p-adic zeta values

Abstract: This is a talk 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).

Google Video

ORGANIZATIONAL MEETING 2:30 - 3:30:

After a 30-minute Overall Sage Status Report by William stein, we will discuss the plan for working groups for the remainder of the workshop.

EVENING REPORTS (7-8)

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.

Google Video

Speaker: Martin Albrecht
Title: Commutative Algebra and Sparse Linear Algebra in SAGE (Singular, PolyBoRi)

Abstract: 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.

20071003_-_commutative_algebra.pdf Google Video

EVENING WORKING SESSION (8pm-?)

MONDAY

MORNING TALK 1

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 on 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.

besser.pdf Google Video

MORNING TALK 2

Speaker: Robert Bradshaw & Kiran Kedlaya
Title: Coleman integration

Abstract: We will discuss the theory of Coleman integration (as referenced in the previous talk), describe an algorithm for computing some Coleman integrals on hyperelliptic curves, and discuss (and perhaps demonstrate) how this is implemented in SAGE. Besides the application to computing p-adic heights, there are also potential applications to finding torsion and rational points on curves over number fields (also due to Coleman); we will say a bit about these too.

coleman.pdf Google Video

AFTERNOON TALKS

Speaker: Mark Watkins
Title: SYMPOW

Abstract: We discuss the SYMPOW package to compute special values of symmetric powers of elliptic curve L-functions. Google Video

Speaker: William Stein
Title: Algebraic Number Theory in SAGE, a Status Report

stein-ant.pdf Google Video

EVENING REPORTS

Speaker: Bill Hart
Title: A short talk on short division : FLINT (Fast Library for Number Theory) a status report by Bill Hart.

Abstract: 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.

Google Video

Speaker: Michael Abshoff
Title: Valgrind Tutorial

Google Video Another version

Speaker: Michael Abshoff
Title: Managing the SAGE development workflow

http://sage.math.washington.edu/home/mabshoff/trac-talk-2007-10-01.tar.gz Google Video

EVENING WORKING SESSION (8pm-?)

TUESDAY

MORNING TALK 1

Speaker: Gonzalo Tornaria
Title: Stark-Heegner points and the Shimura correspondence

Google Video (part 1 of 2) Google Video (part 2 of 2)

MORNING TALK 2

Speaker: Dimitar Jetchev
Title: Computing Heegner points

jetchev.pdf

AFTERNOON TALK

Speaker: Michael Abshoff
Title: [Ap]CoCoALib

EVENING REPORTS

Speaker: Robert Bradshaw
Title: Cython status report

cython-status-07.pdf Google Video

Speaker: Robert Bradshaw
Title: Coercion Status Report

Abstract: In this controversial report, I will describe the "right" way to discover coercion and explain why the idea of extending baserings is wrong.

coercion.pdf Google Video (part 1) Google Video (part 2)

EVENING WORKING SESSION (8pm-?)

WEDNESDAY

MORNING TALK 1 (at Harvard, 9:00-10:00)

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

MORNING TALK 2

Speaker: William Stein
Title: On convergence in the Sato-Tate conjecture

Abstract: This is a talk on convergence in the Sato-Tate conjecture, in particular, it is an application of Sage to studying how quickly convergence happens in the Sato-Tate conjecture; this in fact leads to a new conjecture and new questions. This is joint work with Barry Mazur.

stein-sato-tate.pdf Google Video

AFTERNOON

Speaker: Moderator
Project Wrap-up

Google Video of the Final Status Reports

NUMBER THEORY SEMINAR (at Harvard, 3:00-4:00)

Title: Ranks of Elliptic Curves
Speaker: Mark Watkins
Location: Science Center 507 (Harvard)

EVENING WORKING SESSION:

   Informal working and coding session for people still around (e.g., William Stein, David Roe, etc.)

-  ⇤ ← Revision 18 as of 2007-09-24 23:47:35 → 
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-Deletions are marked like this.
+Additions are marked like this.
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+The times are as follows, unless otherwise stated below. 
{{{
MORNING TALK 1 (9:15 - 10:15)
MORNING TALK 2 (10:30 - 11:30)
AFTERNOON TALK (1-2pm)
DINNER (5-7pm)
EVENING REPORTS (7-8pm)
EVENING WORKING SESSION (8pm-?)
}}}
-Line 4:
+Line 14:
-pm -- [http://www.penangusa.com/location_cambridge_menu_dinein.html Penang] 

{{{
+pm -- Dinner at [[http://www.penangusa.com/location_cambridge_menu_dinein.html|Penang]] in Harvard Square; 57 JFK Street, Harvard Square, Cambridge, MA 02138. We would like to make a reservation; please let William know if you plan to attend.
-Line 11:
+Line 19:
-Speaker: William Stein (or Barry Mazur?)
Title: On convergence in the Sato-Tate conjecture
+{{{
Speaker: William Stein
Title: Computations Related to the Birch and Swinnerton-Dyer Conjecture using Sage
}}}
[[http://wstein.org/talks/20070930-stein-bsd/|Slides]]
[[http://video.google.com/videoplay?docid=7984448761799110577&hl=en|Google Video]]
-Line 15:
+Line 27:
+{{{
-Line 17:
+Line 30:
+}}}
Abstract: 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 $\mathbf Q_p$, 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.

[[http://wiki.sagemath.org/days5/sched?action=AttachFile&do=view&target=padic_arith.pdf|Slides]]
[[http://video.google.com/videoplay?docid=-8817702470712955205&hl=en|Google Video part 1 (of 2)]]
[[http://video.google.com/videoplay?docid=-7834241264390846749&hl=en|Google Video part 2 (of 2)]]
-Line 19:
+Line 38:
+{{{
-Line 20:
+Line 40:
-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 (7-8)
Speaker: William Stein and/or Robert Bradshaw
Title: Algebraic Number Theory in SAGE, a Status Report
+Title: Identities between p-adic multi-polylogs and p-adic zeta values
}}}
Abstract: This is a talk 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). 

[[http://video.google.com/videoplay?docid=-5758635886902061837&hl=en|Google Video]]

ORGANIZATIONAL MEETING 2:30 - 3:30:

After a 30-minute ''Overall Sage Status Report'' by William stein, we will  discuss the plan for working groups for the remainder of the workshop.


EVENING REPORTS (7-8)

{{{
-Line 33:
+Line 56:
+}}}
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. 

[[http://video.google.com/videoplay?docid=2930757134671857575&hl=en|Google Video]]

{{{
Speaker: Martin Albrecht
Title: Commutative Algebra and Sparse Linear Algebra in SAGE (Singular, PolyBoRi)
}}}
Abstract: 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.

[[attachment:20071003_-_commutative_algebra.pdf]] [[http://video.google.com/videoplay?docid=156475786677736141&hl=en|Google Video]]

EVENING WORKING SESSION (8pm-?)
-Line 38:
+Line 75:
+{{{
-Line 39:
+Line 77:
-Title: On the Computation of p-adic Height Pairings on Jacobians of
Hyperelliptic Curves
+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 on 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.

[[attachment:besser.pdf]] [[http://video.google.com/videoplay?docid=1477916588819702201&hl=en|Google Video]]
-Line 43:
+Line 91:
+{{{
-Line 45:
+Line 94:
+}}}
Abstract: We will discuss the theory of Coleman integration (as referenced in the previous talk), describe an algorithm for computing some Coleman integrals on hyperelliptic curves, and discuss (and perhaps demonstrate) how this is implemented in SAGE. Besides the application to computing p-adic heights, there are also potential applications to finding torsion and rational points on curves over number fields (also due to Coleman); we will say a bit about these too.

[[attachment:coleman.pdf]] [[http://video.google.com/videoplay?docid=7414272363294014907&hl=en|Google Video]]

AFTERNOON TALKS
{{{
Speaker: Mark Watkins
Title: SYMPOW
}}}
Abstract: We discuss the SYMPOW package to compute special values of symmetric powers of elliptic curve $L$-functions.
[[http://video.google.com/videoplay?docid=7753480221612447282&hl=en|Google Video]]

{{{
Speaker: William Stein
Title: Algebraic Number Theory in SAGE, a Status Report
}}}
[[attachment:stein-ant.pdf]] [[http://video.google.com/videoplay?docid=3470453209835871513&hl=en|Google Video]]

EVENING REPORTS
{{{
Speaker: Bill Hart
Title: A short talk on short division : FLINT (Fast Library for Number Theory) a status report by Bill Hart.
}}}
Abstract: 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.

[[http://video.google.com/videoplay?docid=-5481874090998683168&hl=en|Google Video]]


{{{
Speaker: Michael Abshoff
Title: Valgrind Tutorial
}}}
[[http://video.google.com/videoplay?docid=-2913379305263249139&hl=en|Google Video]]
[[http://video.google.com/videoplay?docid=3574579568614471949&hl=en|Another version]]

{{{
Speaker: Michael Abshoff
Title: Managing the SAGE development workflow
}}}

http://sage.math.washington.edu/home/mabshoff/trac-talk-2007-10-01.tar.gz [[http://video.google.com/videoplay?docid=-8784589193845902962&hl=en|Google Video]]

EVENING WORKING SESSION (8pm-?)
   

== TUESDAY ==

MORNING TALK 1
{{{
Speaker: Gonzalo Tornaria
Title: Stark-Heegner points and the Shimura correspondence
}}}
[[http://video.google.com/videoplay?docid=1078890468756181537&hl=en|Google Video (part 1 of 2)]] [[http://video.google.com/videoplay?docid=1514873828205448855|Google Video (part 2 of 2)]]


MORNING TALK 2
{{{
Speaker: Dimitar Jetchev
Title: Computing Heegner points
}}}

[[attachment:jetchev.pdf]]
-Line 47:
+Line 159:
-Speaker: Martin Albrecht
Title: Commutative Algebra and Sparse Linear Algebra in SAGE (Singular, PoliBoRi)

EVENING TALKS
Speaker: Bill Hart
Title: FLINT status report
+{{{
-Line 55:
+Line 161:
-Title: Using trac to manage SAGE development workflow

== 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 TALKS
+Title: [Ap]CoCoALib
}}}

EVENING REPORTS
{{{
-Line 74:
+Line 168:
+}}}

[[attachment:cython-status-07.pdf]] [[http://video.google.com/videoplay?docid=8155731528590036456&hl=en|Google Video]]

{{{
-Line 77:
+Line 175:
+}}}
Abstract: In this controversial report, I will describe the "right" way to discover coercion and explain why the idea of extending baserings is wrong.

[[attachment:coercion.pdf]] [[http://video.google.com/videoplay?docid=6579542972326274959&hl=en|Google Video (part 1)]] [[http://video.google.com/videoplay?docid=7943196399220997534&hl=en|Google Video (part 2)]]


EVENING WORKING SESSION (8pm-?)
-Line 80:
+Line 185:
-MORNING TALK 1
+MORNING TALK 1 (at Harvard, 9:00-10:00)

{{{
-Line 84:
+Line 191:
+}}}
-Line 86:
+Line 194:
+{{{
-Line 87:
+Line 197:
-Title: Computing p-adic Invariants of Elliptic Curves and
Applications of Iwasawa theory to BSD
+Title: On convergence in the Sato-Tate conjecture
}}}
Abstract: This is a talk on convergence in the Sato-Tate conjecture, in particular, it is an application of Sage to studying how quickly convergence happens in the Sato-Tate conjecture; this in fact leads to a new conjecture and new questions.  This is joint work with Barry Mazur. 

[[attachment:stein-sato-tate.pdf]] [[http://video.google.com/videoplay?docid=-199443279836975614&hl=en|Google Video]]
-Line 91:
+Line 204:
+{{{
-Line 93:
+Line 207:
-pm NUMBER THEORY SEMINAR:
+}}}
[[http://video.google.com/videoplay?docid=1589461731048191073&hl=en|Google Video of the Final Status Reports]]

NUMBER THEORY SEMINAR (at Harvard, 3:00-4:00)
{{{
-Line 98:
+Line 215:
-}}}

========================================================================

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 $Q_p$, 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. "
+}}}

EVENING WORKING SESSION:
{{{
   Informal working and coding session for people still around (e.g., William Stein, David Roe, etc.)
}}}

Diff for "days5/sched"

Sage Days 5 Schedule

SATURDAY

SUNDAY

MONDAY

TUESDAY

WEDNESDAY