First FOM-Sigma paper

Apparently, the first ever paper to be published by the new FOM journals has been put online today, in FOM-Sigma: a 60 pages paper by Popa and Schnell on “generic vanishing theory”.  [edit:  FOM-Pi also has issued its first paper on the same day: a 77 pages one on "p-adic Hodge Theory", by Peter Scholze. In both cases, the licence used is CC Attribution-NonCommercial-ShareAlike.]  No news yet on the Episciences-Math project.

On a completely different note, there’s an interesting fairly recent interview of Sophie Morel here with a few noteworthy quotes like:

I think that if you want a prize to help people’s careers, then you have to give it to younger people who are still struggling to get a good job.

and:

being hired by Harvard was nice, but being the first woman was just a matter of chance and pretty meaningless as far as I am concerned.

Longevity

Next month, Jean-Pierre Serre will deliver a series of talks in the Distinghuised Lecture Series at the Fields Institute on several new topics. At 86.

Looking for mathematicians who were born before him in the MacTutor website, it seems that Freeman Dyson is still active at 89, and Louis Niremberg, at 88, too.

Very impressive, and certainly as inspiring as centenarians that run, or cycle, or teach fencing.

Perhaps the reader will, one day, do even better, who knows?

Some geometric elegance

From a XIVth century Arabic manuscript (from Gallica), based on a treatise by Theodosius of Bithynia. I do wonder what this particular page says…

Edwards on platonism and patents

This month, there’s a strange but stimulating paper by David A. Edwards in the Notices of the AMS. It’s short and I encourage you to read it and make up your own mind.

He argues that “One should be able to patent anything not previously known to man.“, including algorithms and mathematical formulas — which is currently not allowed on the grounds that “ ‘mere’ recognition of a theretofore existing phenomenon or relationship carries with it no rights to exclude others from its enjoyment“. Edwards sees this as a Platonistic argument, and says that “There is no economic basis for the distinction between discovery and invention“.

 

I personally do not hold Platonistic views at all, and feel that any thoughts human may have are indeed inventions, new ways of describing ‘reality’, and not discoveries of pre-existing things. For instance, nothing satisfies Newton’s laws exactly in the Universe, on the contrary it is a first approximation of some phenomenas in certain cases. And what about recognising that is true? Isn’t there a good case to say that it was true ‘before we noticed it’? No, as far as I’m concerned. It is human notation. You work things out for the first time, you explore consequences of the chosen rules, but before stating them these statements have no status, they are certainly not ‘out there, pre-exisiting’.

So, while I wouldn’t agree with patentable mathematical formulas or physics laws, it wouldn’t be based on Platonistic grounds, but rather on freedom of thought: if author A finds a consequence of a set of axioms that was not known to others before, fine, it enters the realm of actual human thoughts. But A can’t stop others to infer that consequence for themselves later: independently some author B may well write that same formula. What would it mean that B infringed A’s patent on that idea when B never heard of A in the first place?  The only reasonable thing to do is an anteriority claim based on a published paper, and leave open the possibility of renaming the formula ‘the A-B theorem’ if it appears clearly enough that B indeed found it independently (and this of course abounds in the history of science). But certainly not a patent.

 

Mathématiques et finitude

The title of this post is the title of a 539-pages long file by Pierre Lochak (in french), listed at the bottom of his homepage.

I’ve just stumbled upon it, and at first glance it seems to be a mix of historical and philosophical comments, centered around Grothendieck but with lots of other topics too.

If I understand correctly the table of contents at the end, it is in the process of being written and is about half-way through (it stops at page 516 with section 7.3.4 “en cours d’écriture”).

According to the Epilogue, Grothendieck (who turned 85 recently, and lives in a very remote south-western french village) still writes continuously (“il écrit sans relâche”). That should be fascinating material for future generations of epistemologists to one day ponder upon.

MO and FOM-Pi, the new mainstream?

Today on the arXiv, a survey of perfectoïd spaces was posted by their inventor Peter Scholze.

It is all way above my head, but two things are striking from an outsider’s perspective:

- after some comments, the main text starts by “This introduction is essentially identical to a post of the author on MathOverflow” (namely this).

- it lists a forthcoming paper as:  P. Scholze. p-adic Hodge theory for rigid-analytic varieties. 2012. arXiv:1205.3463, to appear in Forum
of Mathematics, Pi. (Possibly the first reference ever to this journal.)

I may be wrong, but perhaps even just 5 years ago this would have refered instead respectively to something like “Letter to X” and “to appear in Ann. Math.“

Math projects at the 2013 Intel STS and 2012 Siemens Competitions

The winners of the 2013 Intel STS Competition have been announced recently.  Nice to see that, again, many math projects made the top 10:

- Hannah Larson ranked 4th, for giving a complete classification of the rank four fusion rings that give rise to fusion categories (see this earlier video about her) ;

- Samuel Zbarsky finished 7th by improving lower and upper bounds on a ratio of path lengths in a high-dimensional Euclidean Geometry problem ;

- Sahana Vasudevan (a former PRIMES student) ranked 10th with her project titled “Minimizing the Number of Carries in the Set of Coset Representatives of a Normal Subgroup” ;

 

Back in december 2012, the Siemens Competition revealed its own winners. No math project got in the top 6 individual, but two teams made the top 6:

- Daniel Fu and Patrick Tan finished 2nd with their project on genetic oscillatory networks.

- Jonathan Tidor and Rohil Prasad ranked 5th for their work on staged self-assembly of Wang tiles.

 

Well done to them all!

International Summer School for Students 2013: apply now!

Following the two successful previous years, there will be a great mathematics summer school for students who are between the last two years of high school and first two years of university.

It will take place in Bremen (Germany) from july, 2 to july, 12.

Application deadline is march, 20, so if you’re interested hurry up!

Also, please spread the word if you know someone that might want to go there.

 

Clay Research Fellows

Since the laureates for 2013 have just been announced, here is the full list of Clay Research Fellows by year (with URLs valid as of february 2013):

2000: Manjul Bhargava, Dennis Gaitsgory, Terence Tao

2001: Roman Bezrukavnikov, Alexei Borodin, Daniel Gottesman, Sergei Gukov, Mircea Mustata

2002: Daniel Biss, Igor Rodnianski

2003: Maria Chudnovsky, Elon Lindenstrauss

2004: Ciprian Manolescu, Maryam Mirzakhani, András Vasy, Akshay Venkatesh

2005: Bo’az Klartag, Ben Green, David Speyer

2006: Artur Avila, Sophie Morel, Sam Payne

2007: Mohammed Abouzaid, Soren Galatius, Davesh Maulik, Teruyoshi Yoshida

2008: Spyros Alexakis, Adrian Ioana, Xinyi Yuan

2009: Sucharit Sarkar

2010: Tim Austin

2011: Peter Scholze

2012: Ivan Corwin, Jack Thorne

2013: Semyon Dyatlov, Aaron Pixton

Cours Peccot

Each year since 1900, the french Fondation Claude-Antoine Peccot picks between 1 and 3 mathematicians under the age of 30 who have already made important advances, and gives them the opportunity to give a few lectures on their research topics, the so-called Cours Peccot  (either at Collège de France, or at École Normale Supérieure).

The list of previous lecturers is basically a who’s who of french mathematics (plus a few non-french lecturers too, from time to time).  Since the most recent lecturers don’t appear on the list yet, here’s what I could reconstruct. I’ve added a link to lecture webpages or handouts when they exist (feel free to mention mistakes if I’ve made any):

2002: Denis Auroux. Thierry Bodineau.
2003: Franck Barthe. Cédric Villani.
2004: Laurent Fargues. Laure Saint-Raymond.
2005: Artur Avila. Stefaan Vaes.
2006: Laurent Berger. Emmanuel Breuillard.
2007: Erwan Rousseau. Jérémie Szeftel.
2008: Karine Beauchard. Gaëtan Chenevier.
2009: Joseph Ayoub. Julien Dubédat.
2010: Antoine Touzé.
2011: Sylvain Arlot. Anne-Laure Dalibard.
2012: Alessio Figalli. Vincent Pilloni.
2013: Valentin Féray. Christophe Garban. Peter Scholze.