tag:blogger.com,1999:blog-69126032879302404512012-01-13T22:34:56.028ZArupnoreply@blogger.comBlogger711100tag:blogger.com,1999:blog-6912603287930240451.post-41506594406020953532011-10-05T18:41:00.005Z2011-10-05T19:06:42.659Z

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

Matildehttp://www.blogger.com/profile/01820633659103015340noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-89913777821677379982011-09-13T17:38:00.004Z2011-09-13T19:30:42.105Z

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

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com4tag:blogger.com,1999:blog-6912603287930240451.post-80392983563069993862011-07-21T12:37:00.014Z2011-07-22T01:13:56.838Z

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

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-46950936630309511142011-01-27T18:51:00.000Z2011-01-27T18:51:32.907Z

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

AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com6tag:blogger.com,1999:blog-6912603287930240451.post-55319138147916555722010-12-31T19:46:00.008Z2011-01-01T13:05:42.549Z

First of all, happy new year to all our readers and user of this blog! Wish you all a great newyear 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

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-85107859430758717042010-03-30T17:04:00.009Z2010-04-01T02:52:30.584Z

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

Matildehttp://www.blogger.com/profile/01820633659103015340noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-49277126950291538852009-12-26T02:48:00.009Z2009-12-27T00:49:46.116Z

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!

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com3tag:blogger.com,1999:blog-6912603287930240451.post-9324712667990127402009-10-07T04:25:00.017Z2009-10-10T13:57:01.125Z

The noncommutative geometry blog is deeply saddened to inform its readers of the passing of Israil Moiseevic Gelfand, one of the most influential mathematicians of the 20th century, on October 5 at the age of 96. Gelfand's monumental contributions to mathematics and science covered many areas including commutative normed rings and functional analysis, representation theory of Lie groups and Lie

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com2tag:blogger.com,1999:blog-6912603287930240451.post-52317807955031071122009-03-29T16:47:00.023Z2009-03-30T19:18:47.363Z

I was in Baltimore last week attending the Jami Conference at JHU which was followed by a two days long workshop on F_1. Both events were coordinated mostly by Katia Consani, with the help of S. Mahanta (and myself). I went to all lectures and feel ready to make some comments for those talks which I had the impression to understand. For now I'll just talk about the first day.The first talk was by

AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com5tag:blogger.com,1999:blog-6912603287930240451.post-59392413231702050142009-01-19T20:42:00.005Z2009-01-25T15:13:36.123Z

In my previous contributions to this blog , I have mentioned how the calculations of Dinesh Thakur and Javier Diaz-Vargas suggested that the nonclassical trivial zeroes of characteristic $p$ zeta functions associated to ${\bf F}_q[t]$ should have the following two properties (where nonclassical means that the actual order is higher than what one would expect from classical theory):1. If a

David Gosshttp://www.blogger.com/profile/01874443969277514500noreply@blogger.com3tag:blogger.com,1999:blog-6912603287930240451.post-17142748501206440272009-01-18T13:57:00.004Z2009-01-20T00:46:55.282Z

In this blog entry, I would like to highlight a remarkable formula due to Dinesh Thakur in the arithmetic of function fields over finite fields. This formula appears in page 5 of his preprint "Power sums with applications to multizeta values and zeta zeros" which can be downloaded athttp://math.arizona.edu/~thakur/power.pdfBefore presenting Dinesh's formula, I will present a little history. Early

David Gosshttp://www.blogger.com/profile/01874443969277514500noreply@blogger.com1tag:blogger.com,1999:blog-6912603287930240451.post-78952094016070057832008-10-29T13:43:00.002Z2008-10-29T13:48:42.923Z

Dear Colleagues: Atiyah has given a very bracing address on "Mind, matter and mathematics". You can obtain a pdf of it athttp://www.rse.org.uk/events/reports/2007-2008/presidential_address.pdfand can read a report on a similar talk athttp://www.dailystar.com.lb/article.asp?edition_id=1&categ_id=2&article_id=97190 My best, David

David Gosshttp://www.blogger.com/profile/01874443969277514500noreply@blogger.com5tag:blogger.com,1999:blog-6912603287930240451.post-90410456872797863882008-10-13T09:26:00.005Z2008-10-13T09:53:39.699Z

Last week there was a meeting on spectral geometry and index theory at the Universidad de Los Andes in Bogotá, Colombia, organized by Alexander Cardona and Jean Carlos Cortissoz. The Encuentro "Geometría Espectral y Teoría del Índice" consisted of four afternoons of lectures and research talks, and this light but effective setup made it a very pleasant meeting. Even more because of the beautiful

Walterhttp://www.blogger.com/profile/18443611486145891072noreply@blogger.com1tag:blogger.com,1999:blog-6912603287930240451.post-18732176832575982792008-10-03T12:39:00.002Z2008-10-03T12:44:06.484Z

The paper "Fun with F_un" by Alain, Katia, and Matilde will appear soon in the Journal of Number Theory. An associated video abstract by Alain can be found athttp://www.youtube.com/user/JournalNumberTheoryorhttp://www.youtube.com/user/AlainConnesAlain's video is a terrific example of what is possible with these video abstracts! My best, David

David Gosshttp://www.blogger.com/profile/01874443969277514500noreply@blogger.com4tag:blogger.com,1999:blog-6912603287930240451.post-33040182221031791632008-09-05T17:31:00.002Z2008-09-05T17:47:09.796Z

In this post, I would like to discuss a really beautiful solution of an open issue in the theory of characteristic p L-series. This solution is in the short paper arXiv:0808.4069 by Sangtae Jeong and is a great illustration of the use of calculus in finite characteristic. I have written this post so that, if you choose, you can just copy it and paste it into a latex file and it will compile.In my

David Gosshttp://www.blogger.com/profile/01874443969277514500noreply@blogger.com1tag:blogger.com,1999:blog-6912603287930240451.post-65957359461961399812008-08-04T15:57:00.005Z2008-08-04T18:14:14.794Z

In a rather ironical manner the first Higgs mass that is now excluded by the Tevatron latest results is precisely 170 GeV, namely the one that was favored in the NCG interpretation of the Standard Model, from the unification of the quartic Higgs self-coupling with the other gauge couplings and making the "big desert" hypothesis, which assumes that there is no new physics (besides the neutrino

AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com20tag:blogger.com,1999:blog-6912603287930240451.post-64642401635950936602008-08-04T01:04:00.002Z2008-08-04T01:18:00.356Z

This is a follow up to the posts of Alain and Katia on the Vanderbiltworkshop this past May. It was a really great conference and I would again liketo thank the organizers for including me.After I returned from the conference, I decided to try to write downwhat I had talked about. In doing that, I finally was able to glimpsecertain underlying symmetries that I had long been looking for. Iwrote

David Gosshttp://www.blogger.com/profile/01874443969277514500noreply@blogger.com2tag:blogger.com,1999:blog-6912603287930240451.post-8182843487887558412008-08-01T18:36:00.011Z2008-08-02T12:16:46.844Z

By AC and K. ConsaniThe second part of the workshop on the interaction between NCG & the field with one element held at Vanderbilt University this past May 15-18, included the presentation of several new results as well as some speculative discussions with topics ranging from number theory and noncommutative/arithmetic geometry to the most recent developments in Hopf-cyclic theory.Within the

AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com1tag:blogger.com,1999:blog-6912603287930240451.post-31851235123320257112008-06-04T15:29:00.007Z2008-06-05T14:04:12.031Z

By A. C. and K. ConsaniOn the second day of the workshop we presented the main results contained in our recent preprint (joint work with Matilde Marcolli) "Fun with F_1". The pdf file is downloadable here. Our main point is to establish a bridge between F_1 and the quantum statistical mechanical system (known as the BC-system) which gives, after passing to the dual system, a spectral realization

AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com8tag:blogger.com,1999:blog-6912603287930240451.post-32084445237694043602008-05-24T14:15:00.007Z2008-06-08T21:34:55.553Z

(by A.C. and K. Consani)Right after the end of the Sixth Annual Spring School/Conference on Noncommutative Geometry and Operator Algebras, a second meeting took place at Vanderbilt University, on May 15-18. This workshop has been dedicated to explore some aspects of several emerging relations linking Noncommutative Geometry and the geometry over the field with one element.In the next weeks, we

AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com3tag:blogger.com,1999:blog-6912603287930240451.post-42755789248148051222008-05-16T03:57:00.002Z2008-05-16T03:59:26.365Z

The Sixth Annual Spring Institute on Noncommutative Geometry and Operator Algebras in Vanderbilt University wrapped up yesterday. Some of the lectures and lecture series are already available online here.

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-27150139773159752962008-04-09T18:33:00.010Z2008-04-13T12:45:14.777Z

There seems to be some inconsistency, mainly in the Internet, in naming one of the main theorems proved by Gelfand and Naimark in their foundational 1943 paper:On the imbedding of normed rings into the ring of operators in Hilbert space. Rec. Math. [Mat. Sbornik] N.S. 12(54), (1943). 197--213.I have seen the result in question referred to as Gelfand-Naimark' or Gelfand's theorem. Also, talking to

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com13tag:blogger.com,1999:blog-6912603287930240451.post-67669141332350517812007-12-06T15:16:00.000Z2007-12-08T14:04:10.036Z

During August 15-30, 2007, a school and workshop on noncommutative geometry took place at the Chern Institute in Nankai University in Tianjin, China. The first two weeks and part of the third week was devoted to a series of mini-courses (5 lectures each) on various aspects of noncommutative geometry. This conference and its success owes a lot to the Chern Institute and to our Chinese friends on

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com2tag:blogger.com,1999:blog-6912603287930240451.post-89269696579428562542007-10-31T16:29:00.000Z2007-10-31T21:05:54.803Z

Katia's last post ended with a provocative question motivated by Grothendieck's description in Récoltes et Semailles of the "heart of the heart" of arithmetic geometry, namely the theory of motives. Her question was formulated like this:--------What is the "heart of the heart" of noncommutative geometry?-------I'll try to explain here that there is a definite "supplément d'âme" obtained in the

AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com13tag:blogger.com,1999:blog-6912603287930240451.post-44262468776266705372007-10-31T08:34:00.001Z2007-10-31T08:54:09.851Z

Let us start this report on this meeting in a light way with a picture, featuring the subject of this blog and David Goss...Connes opened the meeting with a talk on some analogies between two grand challenges in mathematics and physics: On the one hand, the search for a geometric setting in which the methods of Weil's proof of the Riemann hypothesis (RH) for curves over finite fields could be

Walterhttp://www.blogger.com/profile/18443611486145891072noreply@blogger.com1tag:blogger.com,1999:blog-6912603287930240451.post-5988738974106881622007-09-20T19:51:00.000Z2007-09-23T19:48:54.345Z

While updating my post on Hilbert, thanks to Manfred Karbe's e-mails I came across these two very interesting, powerful and engaging pieces on abstraction and instruction in mathematics by Galois. I put these texts here just in case the French website where they are taken from becomes unavailable sometime. I think the ultimate reference for Galois' writings is the book `Écrits et Mémoires

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com1tag:blogger.com,1999:blog-6912603287930240451.post-52572726031203121872007-09-18T19:11:00.000Z2007-09-18T20:18:19.112Z

It is with this fascinating title that A. Grothendieck presents in Recoltes et Semailles (cfr. Promenade à travers une oeuvre ou l'Enfant et la Mère) the subject of motives: the deepest of the twelve research themes around which he developed his "long-run" research program that literally revolutionized the field of algebraic geometry in the decade 1958-68. Motives were envisaged as the "heart of

KC (= Katia Consani)http://www.blogger.com/profile/12442719430556938476noreply@blogger.com1tag:blogger.com,1999:blog-6912603287930240451.post-68945852609828352562007-09-16T15:53:00.000Z2007-09-17T00:28:28.343Z

This seems to be a banner year for books on noncommutative geometry. Leading the pack is ``Noncommutative Geometry, Quantum Fields. and Motives" by Alain and Matilde which will be published by the American Mathematical Society in January 2008. Earlier this year we introduced two other books.Now two other new books that just appeared in the market. Topological and Bivariant K-Theory by Joachim

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com1tag:blogger.com,1999:blog-6912603287930240451.post-33144193360516817542007-09-12T11:57:00.000Z2007-09-20T19:35:39.831Z

With the above words (translation: we must know, we will know), Hilbert ended his 1930 address in Königsberg, at the Congress of the Association of German Natural Scientists and Medical Doctors. A four minute excerpt was broadcast by radio, and is available here. This I believe is one of the earliest audio files of a speech by a mathematician of note, available online.For the original German text

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com6tag:blogger.com,1999:blog-6912603287930240451.post-60368220955683819922007-09-09T19:11:00.000Z2007-09-11T03:16:32.280Z

For the readers who may be interested in the work Alain and I did on renormalization and the Riemann-Hilbert correspondence, as well as in a general introduction to the Connes-Kreimer theory, I noticed recently that the series of lectures of the minicourse we gave two years ago at Vanderbilt University have now been put on You Tube (or Google Video).You can find them here:Lecture 1 (1 h 52 min)

Matildehttp://www.blogger.com/profile/01820633659103015340noreply@blogger.com3tag:blogger.com,1999:blog-6912603287930240451.post-48119709033670048632007-09-05T11:33:00.000Z2007-09-05T11:41:58.131Z

Today the editorial board of the new Journal of K-theory put out a public statement, which we reproduce below:STATEMENT OF THE EDITORS OF THE " JOURNAL OF K-THEORY »After several public statements and news articles regarding the Springer journal "K-theory" (KT), and the new "Journal of K-Theory" (JKT) to be distributed by Cambridge University Press (CUP), the mathematical community has become

AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com16tag:blogger.com,1999:blog-6912603287930240451.post-61288604248580476362007-08-13T09:14:00.000Z2007-09-05T12:30:13.946Z

This "post" is mainly an attempt to see if one can manage to use formulas in the blog and discuss some real stuff somehow. The formulas should be really visible, a bit like with transparencies. So as a pretext, I'll start by discussing an issue related to the basic Ansatz: which gives the operator theoretic line element in terms of the Dirac operator in the general framework of "metric"

AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com5tag:blogger.com,1999:blog-6912603287930240451.post-44994378030324034672007-08-07T07:36:00.000Z2007-08-07T12:29:21.948Z

This just in. The editorial board of `K-theory' has resigned and a new journal titled `Journalof K-theory' has been established. In recent years `K-theory' was published by Springer. `Journal of K-theory' will be published by the Cambridge University Press. The board of editors of the new `Journal of K-theory' has issued an open letter to the mathematics community that we quote in part:``OPEN

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com4tag:blogger.com,1999:blog-6912603287930240451.post-53678142194444738072007-08-03T20:27:00.000Z2007-08-04T08:48:05.065Z

I am just back from a very nice event around Paul Baum's seventies, which took place in Warsaw last Monday, thanks in particular to Piotr Hajac. I have known Paul since the summer of 1980 when we first met in Kingston. I really had, when I first met him, the impression of meeting l'"Homologie en personne". The more I got to know him through our very long collaboration, the better I enjoyed his

AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com1tag:blogger.com,1999:blog-6912603287930240451.post-54910130045830205662007-07-25T13:36:00.000Z2007-07-26T20:54:12.149Z

We should perhaps update this blog more often but we find almost no time to do that! Alain is very busy editing, correcting, and finalizing his book, Noncommutative Geometry, Quantum Fields and Motives, with Matilde Marcolli. This is no easy task given the size and scope of the work. BTW, I hope sometime soon we will have a good and extensive review of this book in this blog. I am also busy

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com6tag:blogger.com,1999:blog-6912603287930240451.post-25013977727004651972007-07-17T11:01:00.000Z2007-07-17T16:40:33.846Z

I am not sure I really know how to make use of a "blog" like this one. Recently I had to write a sollicited paper describing the perspective on the structure of space-time obtained from the point of view of noncommutative geometry. At first I thought that I could just be lazy and after the paper was written (it is available here) just use pieces of it to keep this blog alive during the summer

AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com7tag:blogger.com,1999:blog-6912603287930240451.post-34393439840521441772007-07-10T19:42:00.000Z2007-07-11T06:24:17.664Z

The next step is to understand what is the replacement of the Riemannian paradigm for noncommutative spaces. To prepare for that, and using the excuse of the summer holidays, let me first tell the story of the change of paradigm that already took place in the metric system with the replacement of the concrete "mètre étalon" by a spectral unit of measurement.The notion of geometry is intimately

AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com3tag:blogger.com,1999:blog-6912603287930240451.post-23154599154439965462007-07-03T12:58:00.000Z2007-07-03T13:52:11.280Z

As I explained in a previous post, it is only because one drops commutativity that, in the calculus, variables with continuous range can coexist with variables with countable range. In the classical formulation of variables, as maps from a set X to the real numbers, we saw above that discrete variables cannot coexist with continuous variables.The uniqueness of the separable infinite dimensional

AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com14tag:blogger.com,1999:blog-6912603287930240451.post-34304254278240189522007-06-25T23:49:00.000Z2007-09-07T11:49:30.478Z

Katia Consani has kindly written the following post for the NCG blog. Many thanks to Katia!I like to think that from his grave in St. Petersburg, Euler is probably quite pleased to see how far his studies on ``Analysis Infinitorum'' have been successfully developed in these past 224 years from his death. The book "Introductio in analysis infinitorum"(1748) has been translated into English in 2

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com2tag:blogger.com,1999:blog-6912603287930240451.post-64629387884707749582007-06-22T09:22:00.000Z2007-06-22T15:38:59.871Z

I was recently at the "Euler Festival" in St. Petersburg, for the 300-th anniversary of the birth of Euler.The wonderful hospitality of the great scientists there, such as Ludwig Faddeev, created a perfect atmosphere for the event. With the long evenings, added to the charm of the city, there was plenty of time to try and get in the right mood to get more familiar with some of Euler's thoughts. I

AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com5tag:blogger.com,1999:blog-6912603287930240451.post-56186206227796426462007-06-21T17:32:00.000Z2007-06-21T19:27:14.198Z

The third issue of Journal of Noncommutative Geometry has just appeared. This is a newly established Journal devoted to the subject and its application. In the description of the Journal we read:``The Journal of Noncommutative Geometry covers the noncommutative world in all its aspects. It is devoted to publication of research articles which represent major advances in the area of noncommutative

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-72404013773620908012007-06-13T23:13:00.001Z2007-06-13T23:39:59.345Z

Recently there was some discussion in the n-category cafe about linear algebra and specially about determinants and their place in a linear algebra undergraduate course. The whole discussion was in fact triggered by a rather polemic paper entitled `Down with Determinants' which seemed to suggest that determinants better be introduced in the graduate school first! This `extremist' point of view

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com3tag:blogger.com,1999:blog-6912603287930240451.post-36690597131709832472007-06-06T20:37:00.000Z2007-06-06T21:53:34.162Z

Hi guys, sorry it took me so long to decide to post something. I was at the Chicago conference and I agree that it was a very interesting event. Unfortunately, I did not go to all the talks (I am a bit overloaded with conferences as the moment, so - much as I would like it - I never manage to attend more than a couple of talks a day), so I can only give a very partial overview of what was

Matildehttp://www.blogger.com/profile/01820633659103015340noreply@blogger.com1tag:blogger.com,1999:blog-6912603287930240451.post-37457854067350612332007-06-06T18:30:00.000Z2007-06-07T15:38:37.552Z

I have some feeling of guilt for being late in reporting on the two recent conferences I (partially) attended: one in Vanderbilt, the other in Chicago, and for indulging in lighter stuff like reporting on the (very nice) conference on Pauli and Jung... Sorry, but that was easier.As for the conference in Vanderbilt the slides are available on line, as well as the list of talks. I'll try to write

AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-17384507589737643762007-05-30T18:50:00.000Z2007-06-04T20:54:00.853Z

I just got a very interesting article entitled "A thing of beauty" by Arthur Miller, whom I met in Ascona. The nuance between "beauty" and "simplicity" might be an interesting topic of discussion. In fact an essential point of our joint work (with Chamseddine and Marcolli) on the Standard Model coupled to gravity is to obtain the complicated Lagrangian from a simple principle: the spectral action

AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com5tag:blogger.com,1999:blog-6912603287930240451.post-83760231682209125182007-05-26T12:49:00.000Z2007-05-26T14:07:18.215Z

Thanks to Masoud for keeping the blog alive in the middle of all these trips to conferences. The last one I attended ended today and was dedicated to Pauli's philosophical ideas. It was quite interesting and gave me a great occasion to get a better knowledge of these ideas. An interesting talk was given by Rafael Nuñez "Where does mathematics come from? Pauli, Jung, and contemporary cognitive

AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com12tag:blogger.com,1999:blog-6912603287930240451.post-19277197656109086642007-05-22T01:40:00.000Z2007-05-22T11:41:56.395Z

Telegram sent on June 14, 1954 from physicists Fred Reines and Clyde Cowan to Wolfgang Pauli announcing the detection, for the first time, of neutrinos.Wolfgang Pauli's contributions to physics are too numerous and well known to be recounted here (the exclusion principle, the spin-statistics theorem, and the prediction of the neutrino, to name just a few). His philosophical thoughts on the other

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com1tag:blogger.com,1999:blog-6912603287930240451.post-62456826023781534002007-05-17T16:43:00.000Z2007-05-17T18:10:16.906Z

The FIFTH ANNUAL SPRING INSTITUTE ON NONCOMMUTATIVE GEOMETRY AND OPERATOR ALGEBRAS at Vanderbilt University is over now. Slides of mini courses and talks are gradually becoming available. Check back the middle of this page for the latest updates. In a separate post we hope to have some comments on some of the talks at least.Quite a few other events on noncommutative geometry are scheduled this

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-63713950905463645292007-05-06T02:21:00.000Z2007-05-07T04:18:00.499Z

Professor Dietmar Bisch, chair of the mathematics department at Vanderbilt University, has kindly written the following piece about the newly formed ``Center for Noncommutative Geometry and Operator Algebras (NCGOA)" and its activities for the NCG blog.FIFTH ANNUAL SPRING INSTITUTE ON NONCOMMUTATIVE GEOMETRY AND OPERATOR ALGEBRAS, Vanderbilt University, May 7 to May 16, 2007The Fifth Annual

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com5tag:blogger.com,1999:blog-6912603287930240451.post-44220553677849532352007-04-25T18:33:00.000Z2007-04-25T21:23:44.497Z

Let me first use the opportunity to thank in writing all the participants of the Paris conference. From my side these several days of science meant a lot and the great atmosphere of friendship moved me so deeply.I did my best to make some comments after the talks. In general it is quite difficult to have some real interaction in such circumstances since one rarely keeps in touch with the speakers

AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com1tag:blogger.com,1999:blog-6912603287930240451.post-56589669491441333262007-04-19T00:25:00.000Z2007-04-22T23:47:41.653Z

This is a continuation of a previous post where, to start the discussions, I quoted a portion of a recent interview with Alain (incidentally the full interview is now available and I highly recommend it to the readers of this blog). After a couple of busy weeks now I have some time to follow up on this important question. My aim is to gradually explore some of the themes discussed in the

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com10tag:blogger.com,1999:blog-6912603287930240451.post-89509554024447701522007-04-13T14:18:00.000Z2007-04-14T11:21:29.598Z

It is almost ready! AN INVITATION TO NONCOMMUTATIVE GEOMETRY will be published this summer by World Scientific. The book contains expanded version of some of the lectures delivered during the International Workshop on Noncommutative Geometry at the Institute for Advanced Studies in Physics and Mathematics IPM, Tehran. This was a very successful workshop that attracted more than one hundred

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-60067225882278170732007-04-06T14:00:00.001Z2007-04-14T12:35:39.937Z

The talks for the whole conference have been videotaped and together with the transparencies will be available soon. After a weekend break, the conference moved to the Institut Henri Poincare (IHP) at the heart of Paris on Monday. The talks on Monday were given by Dirk Kreimer ( Diffeomorphism invariance, locality and the residue: a physicist's harvest of a friend's work) ; Ali Chamseddine ( The

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.comtag:blogger.com,1999:blog-6912603287930240451.post-75815524348334590452007-04-02T15:50:00.000Z2007-04-14T12:26:40.806Z

I am in Paris since last Wednesday attending a conference in honor of Alain Connes. The conference started last Thursday at IHES by a talk by Michael Atiyah on "radical new thoughts on the foundations of physics". Atiyah has been proposing for a couple of years that perhaps one should abandon the idea of predicting the future using the formalism of differential equations and initial value

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com5tag:blogger.com,1999:blog-6912603287930240451.post-17328120727965791892007-03-20T17:00:00.000Z2007-03-21T15:40:45.030Z

I will try to describe in loose terms the steps that lead to the emergence of time from noncommutativity in operator algebras. This hopefully will answer the questions of Paul and Sirix (at least in parts) and of Urs.First I'll explain the basic formula due to Tomita that associates to a state L a one parameter group of automorphisms. The basic fact is that one can make sense of the map x --> s(x

AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com9tag:blogger.com,1999:blog-6912603287930240451.post-89789693637147874362007-03-16T01:43:00.000Z2007-03-16T22:47:56.199Z

When we started this blog we promised to gradually build a dictionary (see here and here ) of concepts in use in NCG (= noncommutative geometry). We started with the following listCommutative .................................................Noncommutativefunctions f: X \to C .................operators on Hilbert space; elements of an algebrapointwise multiplication fg.............................

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com15tag:blogger.com,1999:blog-6912603287930240451.post-68214603210005176262007-03-07T20:27:00.000Z2007-03-08T21:59:18.278Z

I guess one possible use of a blog, like this one, is as a space of freedom where one can tell things that would be out of place in a "serious" math paper. The finished technical stuff finds its place in these papers and it is a good thing that mathematicians maintain a high standard in the writing style since otherwise one would quickly loose control of what is proved and what is just wishful

AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com6tag:blogger.com,1999:blog-6912603287930240451.post-20195586175104025342007-03-07T04:01:00.000Z2007-03-07T04:10:42.985Z

The second issue of JNCG is out. Take a look.....

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-71664986687932597122007-03-01T15:09:00.000Z2007-03-03T04:35:59.942Z

MOSAIC SOPHISTICATION A quasi-crystalline Penrose pattern at the Darb-i Imam shrine in Isfahan, IranA few days ago I noticed this article in NYT science section that reports on a recent paper by Lu and Steinhardt in Science (see here and here for the full article; thanks to `thomas1111'). Their abstract says: ``The conventional view holds that girih (geometric star-and-polygon, or strapwork)

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com3tag:blogger.com,1999:blog-6912603287930240451.post-7507939208696585022007-02-27T17:49:00.000Z2007-02-28T02:41:44.552Z

We shall try to highlight papers on, or around, noncommutative geometry as they are posted. (except occasionally, I won't comment on papers.) Let us know if you think a paper is left out..... Here are a few papers posted this month.Cyclic homology with coefficientsCategorical aspects of bivariant K-theory Homological algebra in bivariant K-theory and other triangulated categoriesLectures on

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-44945039905153594512007-02-27T01:55:00.000Z2007-02-27T01:56:21.531Z

I was delighted when Alain asked me to post on this blog and I came uponthe catchy title above. As a newcomer to noncommutative geometry, I amimpressed by the applications of concepts arising originally in physicsto number theory. An excellent instance of this is the expressionof the Riemann zeta function as a partition function in the work ofBost and Connes.For function fields over finite

David Gosshttp://www.blogger.com/profile/01874443969277514500noreply@blogger.com9tag:blogger.com,1999:blog-6912603287930240451.post-199637187934926022007-02-25T17:18:00.000Z2007-02-25T17:38:49.604Z

I would like to discuss the "next entry" in the parallel texts that Masoud was presenting in his post. On the function theory side we are talking about "real and complex variables". A perfect book to get introduced to that is "real and complex analysis" by W. Rudin (McGraw-Hill). It is a classic and remains one of the best entrance doors to the subject. What one learns is the constant interplay

AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com7tag:blogger.com,1999:blog-6912603287930240451.post-32142226150761710952007-02-22T05:02:00.000Z2007-02-23T13:04:48.989Z

Inspired by Alain's post, I would like to draw attention to a kind of dictionary or rather analogy between commutative concepts and their noncommutative counterparts. (for more on the role of analogies in mathematics and the intricacies of this idea see this 1940 letter of Andre Weil to his sister; my title is inspired by this letter too). I say analogy because there can be no exact

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com9tag:blogger.com,1999:blog-6912603287930240451.post-83752065827005822692007-02-19T21:27:00.000Z2007-02-21T14:36:54.451Z

There are two interesting but quite different general discussions about "quality of maths" available on the web... There is the recent paper by Tao on "what is good mathematics?" and Serre's talk on "how to write mathematics badly"...I strongly recommend to listen to Serre's talk which will result for sure in a definite improvement of the writing style of the listener. The talk is clear, funny,

AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com4tag:blogger.com,1999:blog-6912603287930240451.post-10566475576387166752007-02-16T17:20:00.000Z2007-02-16T17:41:28.101Z

In the first paper on "second quantization", namely the paper of Dirac called "The quantum theory of the emission and absorption of radiation" the process of second quantization is introduced and is related again to "integrality". This time it is not the Fredholm index that is behind the integrality but the following simple fact : if an operator a satisfies [a,a*]=1, then the spectrum of a*a is

AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-71760533635937947792007-02-16T07:03:00.000Z2007-02-16T14:31:47.454Z

This has been posted as a comment to Masoud's post. Since it is almost invisible there, I am posting a copy of it here:This topic of "quantization and NCG" is very relevant. The word `quantum', from the beginning, is not so much related to `non-commutativity' but rather to `integrality'. In the word `quantum' there is really this discovery by Planck, of the formula for blackbody radiation,

Arupnoreply@blogger.com2tag:blogger.com,1999:blog-6912603287930240451.post-38177858869611578002007-02-16T05:49:00.000Z2007-02-17T17:43:38.597Z

Normally, you would get an invitation email, requesting you to join this blog page. The email would look like this:One has to click on the link and keep following the directions, which should be routine. However, there is one place I have seen where there might be a bit of confusion. Suppose you are visiting the page http://noncommutativegeometry.blogspot.com and you are not logged into google

Arupnoreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-60006096339130001292007-02-15T16:09:00.000Z2007-02-15T16:36:32.061Z

Two new books on noncommutative geometry recently appeared. An Introduction to Noncommutative Geometry, by J. Varilly is a short (about 100 pages) introduction to metric and spectral aspects of noncommutative geometry. Surveys in Noncommutative Geometry is edited by N. Higson and J. Roe. It is based on lectures given at the Clay Mathematics Institute Instructional Symposium on Noncommutative

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-15513865325573317272007-02-09T13:41:00.000Z2007-02-09T18:19:14.480Z

Perhaps a better title for this series of posts would be ``Quantization and Noncommutative Geometry". This is a huge topic and certainly takes a lot of time and contributions by many people to do justice to the subject. In a nutshell I would say the revolution brought in physics by the advent of quantum mechanics in the hands of Heisenberg, Dirac, Schrodinger and others in the years 1925-1926 is

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com12tag:blogger.com,1999:blog-6912603287930240451.post-41897193348371891962007-02-08T15:04:00.000Z2007-02-09T02:11:54.957Z

The very first issue of Journal of Noncommutative Geometry is now out:http://www.ems-ph.org/journals/jncg/jncg.phpThe Journal is published by the European Mathematical Society publications. There will be four issues per year. Congratulations to all those who took part in this initiative, including authors of the first issue!

Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com2tag:blogger.com,1999:blog-6912603287930240451.post-20765217324003608462007-01-28T11:42:00.000Z2007-01-29T09:34:40.935Z

The content of this blog is available as an atom feed.In order to use it, target your newsreader tohttp://noncommutativegeometry.blogspot.com/feeds/posts/default

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