Wednesday, October 5, 2011

quasicrystals on their way to Stockholm

It has just been announced that this year's Nobel Prize for Chemistry goes to Daniel Schechtman, at Technion, for the discovery of the structure of quasicrystals.

A nice short overview of the topic and of the prize winner achievements can be found on today's Nature News article.

Besides their importance in chemistry, quasicrystal structures have attracted a lot of attention from mathematicians and mathematical physicists, because of the particular property of the spectra of Schrödinger operators on such quasi-periodic structures.

Geometrically, quasi-crystals behave very much like Penrose tilings and, as such, they fit well within the kind of objects that can be treated by noncommutative geometry methods.

There is a substantial literature on quasicrystal and noncommutative geometry, so I am just going to list here a couple of my favorite papers on the topic, for those who may be interested in looking at what has been done with this geometric viewpoint.

- J.Bellissard, B.Iochum, E.Scoppola, D.Testard, "Spectral properties of one-dimensional quasi-crystals". Comm. Math.Phys. 125 (1989) N.3, 527-543.

- J.Bellissard, D.J.L. Herrmann, M. Zarrouati, "Hulls of aperiodic solids and gap labeling theorems". Directions in mathematical quasicrystals, 207–258, CRM Monogr. 13, Amer. Math. Soc., Providence, RI, 2000.

- J. Bellissard, "The noncommutative geometry of aperiodic solids". Geometric and topological methods for quantum field theory (Villa de Leyva, 2001), 86–156, World Sci. Publ., River Edge, NJ, 2003

- M.T. Benameur, H. Oyono-Oyono, "Index theory for quasi-crystals. I. Computation of the gap-label group", J. Funct. Anal. 252 (2007) N.1, 137-170

Also a book I especially like on quasicrystals (though from a more physical and less mathematical perspective) is this:

Enjoy your aperiodic pastimes...

Tuesday, September 13, 2011

Noncommutative Arithmetic Geometry Media Library

I am pleased to announce the recent creation of a new website dedicated to maintain articles, videos, and news about meetings and activities related to Noncommutative Arithmetic Geometry. This new website is maintained by Alain Connes and Katia Consani. The website is still `under construction' and the plan is to gradually add more videos (also from past conferences and meetings), as well as papers and slides.

Thursday, July 21, 2011

Save Feza Gursey Institute

This blog reports on a recent disturbing event that took place at the Feza Gursey Institute in Istanbul. We would like to ask all blog readers and those who are interested in the fate of pure science in Turkey and elsewhere to take action by writing to relevant people whose name appear at the end of this post.

Feza Gursey Institute, Turkey's single theoretical physics and math institute was closed down by TUBITAK, the mother organization to which Feza Gursey Insitute belongs to.

This decision was made by TUBITAK's highest council, named the Scientific Board
on July 9th, was delivered to the Institute on July 11th, and declared that Feza Gursey Institute is going to become a part of the Informatics and Information Safety Center (BILGEM in Turkish)
in Gebze, the main research campus of TUBITAK, by July 15th.

By this decision, the charter of Feza Gursey Institute was changed in two ways:
Structural Changes: As a part of this Information Safety Center,
Feza Gursey Institute is no longer an independent institute, but
rather a department within this cryptology research center.
Scientific Changes: Feza Gursey Institute mission was redefined
to help pure and applied problems of Turkey, etc...

Although it seems that TUBITAK would keep the renowned physicist Feza
Gursey's name for the institute, Institute will be terminated as a
theoretical physics and math institute and will be reinvented as an
applied sciences Institute within Information Safety Center, BILGEM.

We would like to refer you to here for more information about Feza Gursey Institute.

Also, the institute web site offers a wealth of information.

WE would like to ask for your help. Your support in the form of a letter addressed to Turkish Science,
Technology, and Industry Minister, Nihat Ergun,
and TUBITAK's President Prof. Nuket Yetis to reverse the unfortunate
decision to close down (restructure in the words of TUBITAK President)
Feza Gursey Institute would be very valuable to the scientists of Turkey.

You could use the header and the email addresses:

Dear Minister Nihat Ergun,
Ministry of Science, Technology and Industry

Dear Deputy Undersecretary Dr. Husnu Tekin,

Ministry of Science, Technology and Industry
Dear Professor Nuket Yetis,
TUBITAK President,,,

Thursday, January 27, 2011

Talk by Michael Atiyah on February one

On Tuesday February First, at eleven in Salle 5 of College de France, Sir Michael Atiyah will deliver a talk entitled "A Geometor explores the Universe". His abstract is the following:
"In the past decades theoretical physicists have been using ever more sophisticated mathematics to model the universe and its fundamental forces. Quantum Theory and Geometry are the two main ingredients but there are different schools of thought on how to fuse them together.
Einstein, with his success in General Relativity, argued for the primacy of Geometry and Dirac said we should be guided by beauty.  I belong to this camp and am tentatively exploring some new ideas."