tag:blogger.com,1999:blog-69126032879302404512014-04-15T13:46:49.815ZNoncommutative geometryArupnoreply@blogger.comBlogger93125tag:blogger.com,1999:blog-6912603287930240451.post-2787960844198708032014-03-18T18:46:00.002Z2014-03-18T20:20:44.765ZReview of a paper by Gebhard Boeckle and the group S_(q)
So this post is a bit of an experiment. My friends at Math Reviews recently sent me a really interesting Math. Z. paper by Gebhard Boeckle. I spent some time reviewing it and found it contained very interesting results and calculations that pointed, yet again, to some possible underlying action of the group $S_{(q)}$ that I have discussed in other posts here. If you combine it with the new David Gosshttps://plus.google.com/105910031825143642379noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-39033544028717876472014-02-04T01:53:00.002Z2014-02-18T12:54:32.575Zzeta zeroes AND gamma polesThe arithmetic of function fields over finite fields has always been a ``looking-glass'' window into the standard arithmetic of number fields, varieties, motives etc.; sort of ``life based on silicon'' as opposed to the classical ``carbon-based'' complex-valued constructions. It has constantly amazed me, and frankly given me great pleasure, to see the way that analogies always seem to work out inDavid Gosshttps://plus.google.com/105910031825143642379noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-89329906137579732222013-09-08T18:22:00.002Z2013-09-08T18:22:56.125ZTrimester program on Non-commutative Geometry and its Applications
From September-December 2014 there will be a trimester program on Non-commutative Geometry and its Applications at the Hausdorff Research Institute for Mathematics.
There will be four workshops during the trimester:
September 15-19, Non-commutative geometry's interactions with mathematics.
September 22-26, Quantum physics and non-commutative geometry.
November 24-28, Number theory and Walterhttp://www.blogger.com/profile/18443611486145891072noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-27534619671158227072013-09-05T01:38:00.001Z2013-09-05T01:38:57.437ZAnalytic continuation in the blogosphere....Hi. For those interested, I have started another blog at http://dmgoss.wordpress.com/ to cover items that are probably not appropriate (too technical, specialized, etc.) for this wonderful blog.... Best, DavidDavid Gosshttps://plus.google.com/105910031825143642379noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-66285866793377086192013-08-23T07:55:00.002Z2013-08-23T07:55:25.004ZWebsite Noncommutative Geometry and Particle Physics
A new website on noncommutative geometry has been created, connected to the workshop Noncommutative Geometry and Particle Physics organized at the Lorentz Centre in Leiden in October 2013. As this type of workshop only allows for a limited number of participants, this website will form the virtual portal for a wider audience.
It will contain updates during the workshop, documents Walterhttp://www.blogger.com/profile/18443611486145891072noreply@blogger.com1tag:blogger.com,1999:blog-6912603287930240451.post-66734665544122675632013-07-09T19:58:00.003Z2013-07-16T17:08:37.374ZA-expansionsAs I have written about before, the integers Z play a dual role in arithmetic. On the one hand, they are obviously scalars in terms of the fields of definitions of varieties etc.; yet, on the other hand, they are also operators, as in the associated Z-action on multiplicative groups (or the groups of rational points of abelian varieties etc.). This is absolutely so basic that we do not notice it David Gosshttps://plus.google.com/105910031825143642379noreply@blogger.com4tag:blogger.com,1999:blog-6912603287930240451.post-69687938996964052432013-04-19T01:37:00.001Z2013-04-23T15:24:46.419ZWronski, Vandermonde, and Moore!This post is based on a recent letter by Matt Papanikolas outlining some results he has discovered whilst writing a (highly anticipated!) monograph on $L$-values in finite characteristic. In staring at Matt's letter, I realized that he allowed one to relate the big 3 matrices (Wronski, Vandermonde and Moore) in one simple formula which I will present below and then pose a related question.
I David Gosshttps://plus.google.com/105910031825143642379noreply@blogger.com1tag:blogger.com,1999:blog-6912603287930240451.post-56711905525298146172013-01-28T01:19:00.000Z2013-01-28T01:19:53.055ZInformal video series on the Carlitz moduleDear All: My student, Rudy Perkins, and his fellow graduate student, Tim All, are creating an informal video lecture series on the Carlitz module. If you are interested, please check out http://rudyperkins.wordpress.com/ . DavidDavid Gosshttps://plus.google.com/105910031825143642379noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-18093585357829788472013-01-17T20:40:00.002Z2013-01-17T20:40:20.891ZCYCLIC HOMOLOGY AND ARITHMETICCyclic homology has recently revealed its potential in
relation to the description of Serre's Archimedean local factors in the
Hasse-Weil L-function of an arithmetic variety as shown in the paper by
A. Connes and C. Consani : Cyclic homology, Serre's local factors and the lambda-operations.
The elaboration of this topic constitutes one of the two leading themes
of the course that AC is AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-19411326218961461732012-10-30T17:14:00.000Z2012-11-21T13:00:43.176ZTHE MUSIC OF SPHERESThe title of this post, the music of spheres, refers to a talk The music of shapes which I gave in Lille, on the 26th of September, on the occasion of a joint meeting with the Fields Institute. The talk is an introduction to the spectral aspect of noncommutative geometry and its implications in physics.
The starting point is the naive question "Where are we?", or how is it possible to communicateAChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com5tag:blogger.com,1999:blog-6912603287930240451.post-46415243397079727462012-10-13T20:30:00.002Z2012-10-30T16:25:16.803ZCarlitz's formalism and Euler's $\Gamma$-functionIt was always my fondest hope that the arithmetic of function fields in finite characteristic would finally become sophisticated enough so that it could be developed somewhat in tandem with classical arithmetic. In the recent past, this hope appears to becoming real. In particular, I would like to draw your attention to the new preprint by Federico Pellarin arXiv:1210.2490 "On the generalized David Gosshttps://plus.google.com/105910031825143642379noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-35698808441028015492012-08-10T21:56:00.000Z2012-08-10T21:56:29.518ZA DRESS FOR THE BEGGAR ?
Since 4 years ago I thought that there was an unavoidable
incompatibility between the spectral model and experiment. I wrote a
post in this blog to explain the problem, on August 4 of 2008, as soon
as the Higgs mass of around 170 GeV was excluded by the Tevatron. Now 4
years have passed and we finally know that the Brout-Englert-Higgs
particle exists and has a mass of around 125 Gev. InAChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com3tag:blogger.com,1999:blog-6912603287930240451.post-37275561716277081002012-07-31T03:12:00.000Z2012-07-31T03:12:57.849ZAnother occurence of the quasi-character $\chi_t$My first introduction to the theory of Drinfeld modules was in the mid 1970's when I was a graduate student at Harvard. My advisor, Barry Mazur, had heard about them from lectures by Deligne (who, I believe, had previously met Drinfeld in Moscow). In any case, based on his knowledge of elliptic modular curves, Barry asked me whether the difference of two cuspidal points would be of finite order David Gosshttps://plus.google.com/105910031825143642379noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-21326051221121230232012-07-11T01:27:00.001Z2012-07-12T02:05:54.735ZOperator/scalar fusion in finite characteristic and remarkable formulaeLet $E$ be a curve of genus $1$ over the rational field $\mathbf Q$. One of the glories of mathematics is the discovery that (upon choosing a fixed rational point "$\mathbf O$") $E$ comes equipped with an addition which makes its points over any number field (or $\mathbf R$ or $\mathbf C$) a very natural abelian group. (In the vernacular of algebraic geometry, one calls $E$ an "abelian variety" David Gosshttps://plus.google.com/105910031825143642379noreply@blogger.com5tag:blogger.com,1999:blog-6912603287930240451.post-8696075170387523412012-07-05T16:52:00.001Z2012-07-05T16:52:37.829ZHabemus Higgs
Yesterday, the ATLAS and CMS experiments at CERN announced the discovery of a Higgs boson at 125 GeV. Surely, this will become one of the most important discoveries of the century. It also caused quite a few interesting 4th of July parties (for once, with a good justification for the fireworks).
For theoretical physicists, this is as much a good reason of excitement as for the experimentalists.Matildehttp://www.blogger.com/profile/01820633659103015340noreply@blogger.com5tag:blogger.com,1999:blog-6912603287930240451.post-79822758218130462012012-06-28T12:37:00.002Z2012-06-28T12:37:20.449ZJuly 4, 2012: All eyes on CERN!
CERN has announced a Scientific Conference on July 4th to be followed by a press conference immediately after. Rumour and news been spreading in the blogsphere, including here, that hints to a dramatic, and long awaited, announcement of Higgs' discovery during this event! Did they eventually get it? Well, we shall see!Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-72175736119501854022012-06-12T02:23:00.000Z2012-06-17T03:43:38.498ZThe Riemann Hypothesis as a statement about ramificationWhen I was learning algebraic number theory long ago, it was remarked that one did not know how far the analogy between Archimedean local fields and nonArchimedean ones could be pushed. In particular, one did not know whether one should view the extension ${\mathbf C}/{\mathbf R}$ as being ramified or not. For example, the value groups (of the usual absolute value) of both $\mathbf R$ and $\David Gosshttps://plus.google.com/105910031825143642379noreply@blogger.com1tag:blogger.com,1999:blog-6912603287930240451.post-4647383065286781372012-06-09T08:34:00.000Z2012-06-09T09:08:15.790ZSAD NEWSIt is with profound sadness that we learn about the sudden death of Jean Louis Loday
who fell by accident off his sailing boat on June 6th. We loose an outstanding mathematician
with so many great achievements and a wonderful friend of many years.
AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-80081207285992624362012-05-03T02:19:00.000Z2012-05-03T11:36:41.719ZInteractions Between Ergodic Theory, Number Theory and Noncommutative Geometry, Ohio State University
The Department of Mathematics at the Ohio State University, in
conjunction with the Mathematics Research Institute, is
running a program during the 2011-2012 academic year
entitled Interactions Between Ergodic Theory, Number Theory
and Noncommutative Geometry. The first workshop entitled Dynamics on Homogeneous Spaces and Number Theory was held on September 12-16,Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-6563673812171733392012-02-27T07:17:00.002Z2012-02-27T07:21:40.609Z"Mathematics is a novel about nature and humankind"A moving and very inspiring long video interview with Yuri Manin is now available in the series "Oral History Project" of the Simons Foundation: here's the link. Matildehttp://www.blogger.com/profile/01820633659103015340noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-38545282377518141512012-02-21T21:21:00.003Z2012-02-21T21:33:28.021ZGaloisThis is just a very short post for those interested in a basic talk about Galois, his relations with the French mathematicians of his time, and a general introduction to the "theory of ambiguity". The talk is in French, available at http://www.alainconnes.org/fr/links.php
Do not forget to click on the "HD" symbol on the screen to get a better quality of video..AChttp://www.blogger.com/profile/10951419541401211230noreply@blogger.com1tag:blogger.com,1999:blog-6912603287930240451.post-9444489274988338562012-02-10T22:22:00.005Z2012-02-11T00:38:43.188ZA new book: Noncommutative geometry, arithmetic, and related topicsProceedings of the JAMI 2009 meeting on ``Noncommutative geometry, arithmetic, and related topics" Just published by Johns Hopkins University Press is available in the market now.Happy reading!Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com1tag:blogger.com,1999:blog-6912603287930240451.post-41506594406020953532011-10-05T18:41:00.005Z2011-10-05T19:06:42.659Zquasicrystals on their way to StockholmIt 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-89913777821677379982011-09-13T17:38:00.004Z2011-09-13T19:30:42.105ZNoncommutative Arithmetic Geometry Media LibraryI 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 asMasoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com4tag:blogger.com,1999:blog-6912603287930240451.post-80392983563069993862011-07-21T12:37:00.014Z2011-07-22T01:13:56.838ZSave Feza Gursey InstituteThis 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.com0