Abstract: and greatly enhancing -> and greatly enhance

Near bottom of page 3: of all (of all...

Bottom of p3: comma missing between references

1st para, p4: part of general case -> part of the general case

2nd para, p4: For the simple Lie groups (...) naturally break up
into :: doesn't make sense

3rd para, p4: examples of the classical groups from which the
inductive arguments leading to general cases... :: is awkward

4th para, p4: For the computation -> For, the computation :: actually
it's not good practice to start a sentence with "for"

4th para, p4: incredibly huge :: awkward

4th para, p4: Indeed the object to be computed.... :: tense changes in
this sentence a few times

2nd para, p5: will anyway provide :: awkward

3rd para, p5: used compute

2nd para, p6: this lead us -> this led us

3rd para, p7: halfplane -> half plane

A general comment on the section on modular forms (after the
description of what a modular form is). It starts off with some
general hyperbole about the importance of modular forms and the link
to L-series and leaves the reader unsure what the project is. Then it
mentions the general impact that modular forms have on mathematics in
very general terms. Then it lists specific computations which will be
done (this section is very good by the way) .

But I would personally start by making a very clear statement that the
project is for the computation of modular forms and describe what you
mean by "computing" them. Mention what computations have already been
done and why they are insufficient. Then you should mention the impact
of past work, e.g. the Emerton example, then mention the applications.
I would also hint very early on that these important computations have
quite some substance, by giving an abbreviated list of explicit
computations that will be performed, a teaser if you like. That way
instead of starting with very general information, you immediately
mention that the proposal is for very specific important computations.

2nd para, p9: compute as much as possible about :: far too general

3rd para, p9: remove "e.g.", it makes it sound like you don't have a
specific plan of attack, and that is clearly not the case

5th para, p9: did you intend to ask a question or to make a statement,
it seems that "is it" should be, "it is".

The statement about the impact of the degree 2 field computation is
weak. I would say something like, "we hope to pave the way for future
collaborations with researchers in blah, blah, blah. The data we
compute will be used for blah, blah, blah."

para 4, p 11: space before comma

Low amounts of symmetry -> Cases bearing fewer symmetries :: passim

The physics proposal starts off with a description of the physics,
which leads into the description of various problems, which leads
subtly into the mention of an algorithm, then a statement about how
the machines will be used. The proposal needs a clear definite
statement at some point before it mentions "the algorithm" of what the
proposal is specifically for. I think the addition of a single
sentence or paragraph, breaking the flow of thought, will be
sufficient for this.

The statement about the bottleneck in the labeling algorithm is
worrying given that you are asking for multi-core machines. I would
make a statement about the fact that a supercomputer is not a valid
solution to this problem because the problem is not easily
parallelised. Rather the computation should be run in parallel with
other computations on a machine with few nodes, but very fast
processors, such as the one you are asking for.

Likewise the statement about the algorithm to generate the codes is
worrying.

para 6, p 14: have created the currently most efficient methods ::
awkward

para 7, page 14: solve vaguely given problems ??

para 7, page 14: for example the recent problem.... :: sentence
doesn't make grammatical sense

Good luck! It looks like a very exciting proposal and I can't imagine
someone sanely rejecting it.

Bill.






On 11 Jan, 01:47, "William Stein" <[EMAIL PROTECTED]> wrote:
> Hi,
>
> The Screms proposal is now completely done, but it's possible for me
> to make some last minute minor
> typo fixes tomorrow morning.  I've posted the latest version here:
>    http://wstein.org/grants/screms/
>
> If you notice _any_ typos or mistakes at all, definitely let me know.
> The proposal is supposed
> to be perfect right now.
>
>   -- william
>
> --
> William Stein
> Associate Professor of Mathematics
> University of Washingtonhttp://wstein.org
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