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

nihat.ergun@tbmm.gov.tr,

husnu.tekin@sanayi.gov.tr,

nuket.yetis@tubitak.gov.tr,



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."

Friday, December 31, 2010

Quanta of Maths


First of all, happy new year to all our readers and user of this blog! Wish you all a great new
year 2011! Secondly I would like to share with you a piece of information on new books in our beloved subject Noncommutative Geometry. The Quanta of Maths, proceedings of a 2007 Paris conference in honor of Alain will be available shortly (if not yet). Here are several links where you can order a copy/or get more information:
AMS Clay Amazon

Finally here is an appeal to noncommutative geometry community. We are planing to add a new section to this blog. If you have a regular (or almost regular!) NCG and related topics seminar please let us know so that we can create a link to it in this blog. This should help people to follow events in the field more effectively.

Tuesday, March 30, 2010

LHC first collisions: modeling the high-energy world



LHC beams produced the first collisions at 7 TeV yesterday. The event, transmitted live on the CERN webcast is now reported at http://public.web.cern.ch/public/
It is good reason for celebration for all those who have been, in one way or another, involved in the study of models for elementary particle physics. It will still take time before some new physics will be detected. The best possible scenario one might envision is that what will be seen does not correspond to any of the currently available theoretical models, as that would definitely usher a major revolution in our way of thinking of high-energy physics. A more moderate expectation is that some of the currently predicted scenarios will be verified: for example, some of the supersymmetric partners of Standard Model particles may be detected.
At least we all expect the Higgs particle to be seen: at what energy it will show up will have theoretical consequences, possibly excluding some of the theoretical scenarios currently considered.

In view of the specific Noncommutative Geometry theme of this blog, one can take this occasion to point out the recent very interesting paper of Thijs van der Broek and Walter van Suijlekom, "Supersymmetric QCD and noncommutative geometry", which extends the particle physics models based on NCG to include the QCD sector of the MSSM, available at http://arxiv.org/abs/1003.3788

There has been also a certain amount of recent activity around the theme of cosmological applications of NCG models of particle physics, with a conference that took place in mid December at the IHES. Models of the very early universe can be obtained by considering the spectral action at unification as a boundary condition and allow the gravitational terms to evolve according to the RGE flow of the corresponding particle physics model through their coupling at unification with the Yukawa parameters via the coordinates of the moduli space of Dirac operators on the fiber noncommutative space. This only provides cosmological models for the epoch between the unification and the electroweak scale, where, however, one can see some inflation scenarios that are specific to this model, see http://arxiv.org/abs/0908.3683.
In terms of testable cosmological prediction, this allows for a modified evaporation law of primordial black holes. A better way to obtain cosmological models from NCG that are not
limited to the very early universe, and can therefore be compared more directly with available cosmological data is in preparation (soon to be released)...

Addendum: after this momentary noncommutative indulgence, let me return briefly to more concrete LHC stuff. A very good recent account of LHC physics is given in the collection of essays published in the volume "Perspectives on LHC physics", edited by Gordon Kane and Aaron Pierce (World Scientific, 2008). It makes a very good reading for anyone interested in getting a short but very informative overview of the main directions in which LHC research is going to develop in the coming months. Just to mention briefly some of the contributions in the volume: a good account of the layout and structure of the Atlas and CMS detectors is given in the paper written by my colleague Maria Spiropulu and by Steinar Stapnes. An interesting discussion of dark matter candidates and their possible occurrence in LHC events is given by Pierce and also touched upon in a few other chapters. The section contributed by Giudice on naturalness is very well presented, I quite enjoyed it. Another nice contribution, again by Maria Spiropulu, this time with Lykken, discusses the problem of "look-alikes" namely different competing models that predict the same inclusive missing energy excess for a given integrated luminosity, in the same detector. One of the main tasks of LHC physics is the disambiguation of these look-alikes, after the models that are ruled out by the expriment have been eliminated. The description of the general approach and strategy for dealing with the look-alike problem is a particularly interesting part of the book. I am not going to spoil the reader's fun by giving away too much of the plot, I simply recommend it as a very good side reading to accompany the parties and celebrations that took place in the last couple of days around the LHC first collisions.



Saturday, December 26, 2009

Basic Noncommutative Geometry


Well, finally BNCG is published now. You can check its cover here. The book is published by the European Mathematical Society Publishing House.

Happy holidays to everyone!