“Secret” notes of Grothendieck to be digitized

Apparently the archive of Grothendieck’s “scribbles” left at Montpellier are now in the process of being digitized and made available online. A tiny collection of 20 000 pages!

Latest news on the Global Digital Library for Mathematics Research

See this brief note in the AMS Notices, describing a 100-page report with super-interesting ideas for the upcoming “21st Century Global Library of Mathematics Research”. Here is a copy of the full-text report.

New reference manager colwiz looks great for mathematics

Over the years I have tried out (and discarded) a number of reference managers, including Papers for Mac, Mendeley, Bibdesk, and Zotero. Very recently, thanks to a tip by Magnus Carlsson, I finally found one which actually seems to be doing what I want it to do: Colwiz. Here are some of the reasons I like it:

– Articles are stored in the cloud AND on my own computer. I really want both.

– Everything just works, even if you’re not a super-hacker like Andrew Stacey.

– I can easily import (lots of) references from MathSciNet (still not possible in Mendeley, which is why I once posted my angriest online comment ever on their feedback page). For example, I just imported references to all articles ever written by Gillet and/or Soulé in less than a minute.

– Colwiz automatically includes links (via doi and also via MathSciNet) to online versions of the article. I think this is brilliant.

– The desktop application apparently does not automatically mess up my own folders and naming of files.

– It’s free (at least as long as you don’t want more than 2 or 3 GB of pdf articles in the cloud).

– They have apps for iPhone, iPad, and Android.

– It’s designed for collaboration.

So far I haven’t discovered any major drawbacks. I doubt that their e-reader handles djvu files, and it seems (unless I’ve missed it) that you search in your own references on general keywords only, without the option to use fields like journal name, time interval etc.

Finally, some links to related things: A MathOverflow question on tools for organizing papers. Wikipedia’s rather complete list of reference managers. Konrad Voelkel’s blog, where he has written on managing papers, managing metadata, and much more.

Iwasawa theory resources

Iwasawa theory is a branch of number theory with important applications to class groups of number fields and to conjectures on special values of zeta functions. Here are some starting points for learning more about this.

(You might find other references at Wikipedia and in this general MathOverflow question.)

Book references:

• Lang: Cyclotomic fields I and II (Google Books)
• Washington: Introduction to cyclotomic fields (Google Books)
• Neukirch, Schmidt, Wingberg: Cohomology of number fields (Google Books)
• Coates and Sujatha: Cyclotomic fields and zeta values
• Iwasawa Collected Papers (2 volumes)
• Noncommutative Iwasawa Main Conjecture over Totally Real Fields (SpringerLink)

Surveys and introductions online:

Manfred Kolster: K-theory and arithmetic (Very nice basic introduction to zeta values and Iwasawa theory)

The Kato ICM talk 2006

Introductory notes by Jim L. Brown

Surveys of Sujatha:

• The Main Conjecture (with Coates)
• On the mu-invariant

Surveys of Venjakob:

• From the BSD over the ETNC to noncommutative Iwasawa theory
• From classical to noncommutative Iwasawa theory

A survey of Greenberg. Other surveys, and a book draft, on Greenberg’s webpage.

Matthias Flach surveys:

• The equivariant Tamagawa number conjecture: A survey
• Iwasawa theory and motivic L-functions

A survey by Mitchell from the Handbook of K-theory, on Iwasawa theory and homotopy theory. (See also an interesting blog post of Eric Peterson here, for some possible connections with chromatic homotopy theory)

For noncommutative Iwasawa theory, here are some additional key papers:

• Fukaya and Kato: A formulation of conjectures on p-adic zeta functions in noncommutative Iwasawa theory
• The five-author paper
• Kakde: The main conjecture of Iwasawa theory for totally real fields from arXiv Front: math.KT by Mahesh Kakde. Some of this is reviewed in arxiv preprints by Venjakob and/or Schneider.
• Skinner and Urban: The Iwasawa main conjecture for GL2
• Various papers of David Burns
• The Bertolini-Darmon paper in Annals
• Malte Witte: Noncommutative Main Conjecture of Geometric Iwasawa Theory

Finally, a list of all papers on MathSciNet labelled with subject code 11R23 (Iwasawa theory), the latest papers on arXiv, and a MathOverflow search on “Iwasawa”.

Free access to all Elsevier material for postdocs between jobs

If you are a postdoctoral researcher between jobs, you can apply for free access to all Elsevier/ScienceDirect scholarly articles here. It seems like all you need is a letter on official letterhead from your last institution, and what you (might?) get is free access for a 6-month period, with a personal access code. Note that you have to apply before Aug 31st! Probably this is something they’re experimenting with partly in response to criticism and boycott, but regardless of your opinion on Elsevier and the boycott debate, access to “their” articles might be useful.

Postdoc position in motivic homotopy theory in Regensburg

The following was posted a month ago to the ALG-TOP mailing list. I haven’t been able to find an application deadline online.

Dear Topologists,this is to invite applications for a

3+3 years PostDoc position at the University of Regensburg,

to be filled by November 1st, 2013 or thereafter.
We are seeking to hire a candidate with a strong research record
in (motivic) homotopy theory or a closely related area.
Teaching duties and salary are competitive.
An exact copy of the position to be filled is currently held by David Gepner, who
kindly agreed to provide further information upon request:

[Email address removed, see Gepner’s webpage]

Obviously, you are equally welcome to turn directly to me with any questions, or
to send an electronic application:

[Email address removed, see Naumann’s webpage]

Looking forward to hearing from you,

Kind regards,

Niko Naumann

Grothendieck anagram

Looking back on the mathematical year 2012, the most exciting thing happening was probably Mochizuki‘s work on the abc conjecture. Something I had hoped to see during 2012, was the writings of Grothendieck, restored to the Grothendieck circle website. Sadly, this has not happened, as Grothendieck himself apparently is opposed to it. However, it is not clear (to an outsider) if he is opposed to having a website dedicated to his memory and/or publishers making money out of his writings, or if he is actually opposed to his hardcore algebraic geometry texts being made available for free to interested mathematicians. Looking carefully at the name Alexander Grothendieck, one observes that permuting the letters yields the sentence “Hardcore EGA, extend link!”. Although not a decisive argument in the moral/legal debate over Grothendieck’s letter, perhaps it means something 😉

One a similar note, the sentence “hi’ risk abstract banana hack” is an anagram of “Banach-Tarski”, while “Plain Anarchy Got Us! Shriek! Ahhh!!” is an anagram of “Hartshorne playing shakuhachi”.

Finally, a little anagram puzzle for those of you who need a small recreational break (can also be used as homework for students you for some reason do not like). Let n be a positive integer, and let S be the set of integers between zero and n (inclusive). Let N be the number of anagrams expressing valid arithmetic equalities between elements in the set S. Example: Twelve plus one = eleven plus two. Try to compute N for small values of n. Do you see a pattern? How does N grow with n? What happens if you replace the word “integer” with the word “rational number with bounded height”?

Happy New Year 2013!

Video lectures on Fundamental groups, non-abelian cohomology, and diophantine geometry, by Minhyong Kim

These lectures were delivered in February 2012 at IHES.

Some of the same content can be found in documents on Kim’s webpage, under Expository Essays.

Postdoc position in Milano

From an email by Luca Barbieri-Viale:

There are post-doc positions “assegno di ricerca” here in Milano for 2 years (up to 4 after renewal). The best research projects among several subjects will be selected. One subject is “Arithmetic geometry, motives and homotopy theory of schemes”. Description: “Comparison theorems for cohomology theories. Motivic cohomology and its applications in arithmetic geometry. Galois representations, modular forms and families. Applications to the study of varieties and motives over local and global fields.”

Deadline for application February 15, 2012.
See this web page for more info and how to apply.

Lecture notes on perfectoid spaces

Today Peter Scholze finished his IHES lecture series on perfectoid spaces and the weight-monodromy conjecture. The complete lecture notes are now available on his webpage, and video will probably become available here.