- June 14, 2009: The documents "For John Stallings" [PDF]
and "For Raoul Bott" [PDF] were added to the
remembrance pages.
- May 29, 2009: I wrote a brief
response [PDF]
to a question posed by Phil Davis and David
Mumford: "What should a professional mathematician know?"
- May 19, 2009: I participated in a panel on Number Theory and Logic at the
MAMLS@Harvard conference (May 9 2009).
Here are my notes [PDF], entitled:
Connections between Logic and Number Theory.
- May 19, 2009: I gave a brief talk to the "Friends of Harvard Mathematics" on May
5 2009 about Number Theory. Here are my notes [PDF] for that talk.
- Apr. 25. 2009: In the article Ranks of twists of elliptic curves and Hilbert's Tenth Problem
[Arxiv PDF],
Karl Rubin and I study the variation of the 2-Selmer rank in families of quadratic
twists of elliptic curves over arbitrary number fields.
It follows from our results that if the Shafarevich-Tate conjecture holds, then Hilbert's Tenth
Problem has a negative answer over the ring of integers of every number field.
The projects page has more details.
- Mar. 8, 2009: first draft of a text
"On time (in mathematics and literature)" for an up-coming conference in Comparative
Literature. [PDF]
- Dec. 19, 2008: I wrote an essay entitled Visions, Dreams, and Mathematics
[PDF]
- May 16, 2008: Here are some notes [PDF]
about Imagination and Mathematics that I wrote to prepare myself for a
public event
at the Philoctetes Center in New York City on May 13, 2008.
- January 11, 2008: the article "Mathematical Platonism and its Opposites" was published in the June 2008 European Mathematical Newsletter (pp.19-21).
It is is available here as a [PDF] file.
For a discussion of this article and related ones see
this website.
- Nov. 20, 2007: My article "How did Theaetetus prove his Theorem?"
has now been published in "The Envisoned Life: Essays in honor of Eva Brann" (eds:
P. Kalkavage, E. Salem) Paul Dry Books, Philadelphia, 2007.
[PDF].
- Sep. 17, 2007: A revised version [PDF],
dated Jul 29, 2006 of the article "When is one thing equal to some other thing?"
- Aug. 7, 2007:
The article of Karl Rubin, Alice Silverberg and Barry Mazur with title
"Twisting commutative algebraic groups" is available
on ArXiv
and has been published in the Journal of Algebra 314 (2007) 419-438.
For more details, see my projects page.
- Aug. 7, 2007: The articles
Finding large Selmer rank via an arithmetic theory of local constants
and Growth of Selmer rank in nonabelian extensions of number fields
with Karl Rubin are now available
on ArXiv
For more details, see the projects page.
- Aug. 7, 2007:
A survey article
"Average ranks of elliptic curves: Tension between data and conjecture"
that I wrote with Baur Bektimirov, William Stein, and Mark
Watkin appeared in the Bulletin of the American Mathematical Society 44 (2007), 233-254.
- Aug. 7 2007:
I have written an article with Frank Calegari on topics related to eigenvarieties
for GL2 over quadratic imaginary fields. A preprint of this article, entitled,
"Nearly Ordinary Galois Deformations over Arbitrary Number Fields"
is available here on arXiv.org.
- Aug 7. 2007:
The article of Barry Mazur and Karl Rubin, "Finding large Selmer Groups"
is available on Arxiv.
It will appear in the Annals of Mathematics.
- Sept. 5, 2006:
A Nature
article ([NATURE Vol 443, 7 September 2006) [PDF]
about the recent work on the Sato-Tate Conjecture (with
computations by William Stein).
Here is a longer version of this,
entitled finding meaning in error terms which started as the text of a lecture I
gave in the Current Developments in Mathematics section of the AMS winter meeting in New
Orleans in January 2007.
- June 21, 2006: See expository article
for a remark on "About the cover: Diophantus's Arithmetica" [PDF 10 Meg]
(7/2006 of Bull. AMS).
- February 5, 2006: Some notes for my basic notions
seminar (now called
Faculty Colloquium) on Functional equations, signs, and parity
on Monday February 6 are
here [PDF].
- November 20, 2005:
"Pourquoi les nombres premiers?" appeared in the
August-October 2005 issue of "Les Dossiers de la Recherche"
[PDF].
- September 8, 2005: Preprint
"Computation of p-Adic Heights and Log Convergence"
([pdf]). For more information, see
the projects page.
|
Prof. Barry Mazur