tag:blogger.com,1999:blog-69126032879302404512015-01-22T01:11:14.985+00:00Noncommutative geometryArupnoreply@blogger.comBlogger101125tag:blogger.com,1999:blog-6912603287930240451.post-61655473105086659312015-01-02T17:45:00.000+00:002015-01-02T17:45:42.093+00:00QUANTA OF GEOMETRYThis is a short update on the post called "particles in quantum gravity",
there were interesting comments and rather than answering them in the
blog i just want to point to a long and detailed talk which I gave in the
Hausdorff Institute in Bonn in December and which is now available on YouTube.
In any case this is a good occasion to wish you all a
HAPPY NEW YEAR 2015!Alain Conneshttps://plus.google.com/109079449189755445238noreply@blogger.com1tag:blogger.com,1999:blog-6912603287930240451.post-26142917610457443002014-12-12T02:27:00.002+00:002014-12-17T22:09:33.320+00:00The Digit PrincipleDavid Gosshttps://plus.google.com/105910031825143642379noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-33588629303698001002014-11-09T16:36:00.000+00:002014-11-09T16:36:53.317+00:00PARTICLES IN QUANTUM GRAVITYThe purpose of this post is to explain a recent discovery that we did with my two physicists collaborators Ali Chamseddine and Slava Mukhanov. We wrote a long paper Geometry and the Quantum: Basics which we put on the arXiv, but somehow I feel the urge to explain the result in non-technical terms.
The subject is the notion of particle in Quantum Gravity. In particle physics there is a well ACnoreply@blogger.com7tag:blogger.com,1999:blog-6912603287930240451.post-78634279450593853382014-08-26T12:39:00.000+00:002014-08-26T12:39:38.352+00:00Differentiation and the missing Kummer congruenceDavid Gosshttps://plus.google.com/105910031825143642379noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-81869375565450036792014-08-13T03:04:00.000+00:002014-08-13T03:04:53.944+00:00Fields Medals 2014: Maryam Mirzakhani, Martin Hairer, Manjul Bhargava, Artur AvilaCongratulations to all 2014 Fields medalists! Very well deserved and also really nice to see a woman wining a Fields medal for the first time ever (and of course I am specially delighted that she has the same undergraduate alma mater, Sharif University, as I! Quanta magazine has a coverage of all four winners Avila, Bhargava, Hairer, Mirzakhani.
It was a bit unusual to see the results Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-33611532029976756552014-07-05T19:03:00.000+00:002014-08-05T14:49:54.872+00:00Lectures on VideoI would like to draw your attention to the following lectures just posted on youtube
1. Alain Connes: Arithmetic Site
Update: and a related interview where some of the relevant ideas in topos theory and the impact of Grothendieck is discussed.
2. Ali Chamseddine: Spectral Geometric Unification
Masoud Khalkhalihttp://www.blogger.com/profile/03769072750559219167noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-31223015150320708072014-06-05T13:30:00.000+00:002014-06-05T13:30:40.745+00:00Announcement book "Noncommutative Geometry and Particle Physics" by Walter van Suijlekom
My book "Noncommutative Geometry and Particle Physics" is due to appear this summer with Springer:
This textbook provides an introduction to noncommutative geometry and presents a
number of its recent applications to particle physics. It is intended
for graduate students in mathematics/theoretical physics who are new to
the field of noncommutative geometry, as well as for researchers in
Walterhttp://www.blogger.com/profile/18443611486145891072noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-66959374225491687652014-06-04T13:11:00.001+00:002014-06-04T13:11:54.254+00:00Quotes from Alain Connes' lecture on the spectral Standard Model at Radboud University Nijmegen
Alain Connes: “Change of paradigm unit of length” (video)
Alain Connes: “What is a noncommutative space and its group of symmetries” (video)
Alain Connes: “Spectral action, Yang-Mills theory” (video)
Alain Connes: “Derivation of the Standard Model from noncommutative geometry” (video)
Walterhttp://www.blogger.com/profile/18443611486145891072noreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-2787960844198708032014-03-18T18:46:00.002+00:002014-03-18T20:20:44.765+00:00Review 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-39033544028717876472014-02-04T01:53:00.002+00:002014-02-18T12:54:32.575+00:00zeta 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-89329906137579732222013-09-08T18:22:00.002+00:002013-09-08T18:22:56.125+00:00Trimester 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-27534619671158227072013-09-05T01:38:00.001+00:002013-09-05T01:38:57.437+00:00Analytic 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-66285866793377086192013-08-23T07:55:00.002+00:002013-08-23T07:55:25.004+00:00Website 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-66734665544122675632013-07-09T19:58:00.003+00:002013-07-16T17:08:37.374+00:00A-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-69687938996964052432013-04-19T01:37:00.001+00:002013-04-23T15:24:46.419+00:00Wronski, 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-56711905525298146172013-01-28T01:19:00.000+00:002013-01-28T01:19:53.055+00:00Informal 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-18093585357829788472013-01-17T20:40:00.002+00:002013-01-17T20:40:20.891+00:00CYCLIC 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 ACnoreply@blogger.com0tag:blogger.com,1999:blog-6912603287930240451.post-19411326218961461732012-10-30T17:14:00.000+00:002012-11-21T13:00:43.176+00:00THE 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 communicateACnoreply@blogger.com5tag:blogger.com,1999:blog-6912603287930240451.post-46415243397079727462012-10-13T20:30:00.002+00:002012-10-30T16:25:16.803+00:00Carlitz'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-35698808441028015492012-08-10T21:56:00.000+00:002012-08-10T21:56:29.518+00:00A 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. InACnoreply@blogger.com3tag:blogger.com,1999:blog-6912603287930240451.post-37275561716277081002012-07-31T03:12:00.000+00:002012-07-31T03:12:57.849+00:00Another 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-21326051221121230232012-07-11T01:27:00.001+00:002012-07-12T02:05:54.735+00:00Operator/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-8696075170387523412012-07-05T16:52:00.001+00:002012-07-05T16:52:37.829+00:00Habemus 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-79822758218130462012012-06-28T12:37:00.002+00:002012-06-28T12:37:20.449+00:00July 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-72175736119501854022012-06-12T02:23:00.000+00:002012-06-17T03:43:38.498+00:00The 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.com1