Motivic stuff

Cohomology, homotopy theory, and arithmetic geometry

Latest news on the Global Digital Library for Mathematics Research

Posted by Andreas Holmstrom on July 19, 2014

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.

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New reference manager colwiz looks great for mathematics

Posted by Andreas Holmstrom on July 11, 2013

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.

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Iwasawa theory resources

Posted by Andreas Holmstrom on July 9, 2013

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:

Surveys of Venjakob:

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

Matthias Flach surveys:

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:

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”.

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Free access to all Elsevier material for postdocs between jobs

Posted by Andreas Holmstrom on July 8, 2013

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.

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Postdoc position in Oslo (topology including motivic homotopy theory)

Posted by Andreas Holmstrom on April 17, 2013

Application deadline 3 May. Quoting from the ALG-TOP mailing list:

Dear Topologists
There is a vacant position as postdoctoral fellow for 2 years from September 2013 within the project “Topology in Norway”.
The project is a cooperation between research groups at the University of Bergen, the University of Oslo, and the Norwegian University of Science and Technology in Trondheim. See  http://www.jobbnorge.no/job.aspx?jobid=92733 for more details (there  is a link to the english version in the upper right corner).
The application procedure is fully electronic via the above website.
Closing date for application: 3 May 2013
The aim of this postdoctoral project is to perform research and aid in the supervision of graduate students within the program “Topology in Norway”. The successful candidate will join one of the teams working on various aspects of algebraic topology, including stable homotopy theory, manifold topology, algebraic K-theory, and motivic homotopy theory. For more information about the aims and scope of this program, see the link to “Project description” on http://www.uib.no/People/csc021/TiN.html
Please contact me if you have any questions.
Best wishes,
Christian Schlichtkrull
I removed Christian’s email address, but it can be found here.

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Postdoc position in motivic homotopy theory in Regensburg

Posted by Andreas Holmstrom on April 6, 2013

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

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Two new blogs: DZB and Chromotopy

Posted by Andreas Holmstrom on April 1, 2013

Just wanted to recommend two blogs that I discovered quite recently. One is DZB’s blog, where I learnt about the really cool Database of L-functions, modular forms, and related objects. The other one is Chromotopy, where I particularly enjoy the posts of Eric Peterson. A few sample posts from Eric: Iwasawa theory for chromatic localizations, a series of posts on the Devinatz-Hopkins-Smith paper, and Bundles for adults.

Posted in Random things found on the web | Tagged: , , , , | 1 Comment »

Grothendieck anagram

Posted by Andreas Holmstrom on January 6, 2013

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!

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A long list of postdoc opportunities

Posted by Andreas Holmstrom on June 7, 2012

Having been through the process of finding and applying for postdoc positions in Europe over the last couple of years, here is now the big list that I wished someone had given me a few years ago.

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

Posted by Andreas Holmstrom on June 6, 2012

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.

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