
Last fall, Matilde Marcolli gave a course at CalTech entitled Oral Presentation: The (Martial) Art of Giving Talks. The purpose of this course was to teach students “how to effectively communicate their work in seminars and conferences and how to defend it from criticism from the audience”. The lecture notes contain basic information on the… Read more »

Previously, we have recalled comparisons between approaches to define a geometry over the absolute point and arthistorical movements, first those due to Yuri I. Manin, subsequently some extra ones due to Javier Lopez Pena and Oliver Lorscheid. In these comparisons, the art trend appears to have been chosen more to illustrate a key feature of… Read more »

Last time we did recall Manin’s comparisons between some approaches to geometry over the absolute point $\pmb{spec}(\mathbb{F}_1)$ and trends in the history of art. In the comments to that post, Javier LopezPena wrote that he and Oliver Lorscheid briefly contemplated the idea of extending Manin’s artsydictionary to all approaches they did draw on their Map… Read more »

This is a belated response to a MathOverflow exchange between Thomas Riepe and Chandan Singh Dalawat asking for a possible connection between Connes’ noncommutative geometry approach to the Riemann hypothesis and the Langlands program. Here’s the punchline : a large chunk of the ConnesMarcolli book Noncommutative Geometry, Quantum Fields and Motives can be read as… Read more »

In the wake of a colleague’s suicide and the suicide of three students, Matilde Marcolli gave an interesting and courageous talk at Caltech in April : The dark heart of our brightness: bipolar disorder and scientific creativity. Although these slides give a pretty good picture of the talk, if you can please take the time… Read more »

I really like Matilde Marcolli’s idea to use some of Jackson Pollock’s paintings as metaphors for noncommutative spaces. In her talk she used this painting and refered to it (as did I in my post) as : Jackson Pollock “Untitled N.3”. Before someone writes a post ‘The Pollock noncommutative space hoax’ (similar to my own… Read more »

The general public expects pictures from geometers, even from noncommutative geometers. Hence, it is important for researchers in this topic to make an attempt to convey the mental picture they have of their favourite noncommutative space, … somehow. Two examples : This picture was created by Shahn Majid. It appears on his visions of noncommutative… Read more »

A feeble attempt to translate the Marcollipost by the ‘wiskundemeisjes’.

At the MaxPlanck Institute in Bonn Yuri Manin gave a talk about the field of one element, $\mathbb{F}_1 $ earlier this week entitled “Algebraic and analytic geometry over the field F_1”. Moreover, Javier LopezPena and Bram Mesland will organize a weekly “F_un Study Seminar” starting next tuesday. Over at Noncommutative Geometry there is an Update… Read more »

There are only a handful of human activities where one goes to extraordinary lengths to keep a dream alive, in spite of overwhelming evidence : religion, theoretical physics, supporting the Belgian football team and … mathematics. In recent years several people spend a lot of energy looking for properties of an elusive object : the… Read more »

In the series “Noncommutative geometry and the Riemann zeta function” we give an introduction to the BostConnes algebra. We describe its relation to adeles/ideles and to KMSstates leading to the zetafunction as the partition function.

MacBookAir? Is this really the best Apple could come up with? A laptop you can slide under the door or put in an envelop? Yeez… Probably the hotairbook is about as thick as an iTouch. The first thing I did was to buy a leather case to protect the vulnerable thing, making it as thick… Read more »

Here a list of saved pdffiles of previous NeverEndingBooksposts on geometry in reverse chronological order.

Yesterday, Yuri Manin and Matilde Marcolli arXived their paper Modular shadows and the LevyMellin infinityadic transform which is a followup of their previous paper Continued fractions, modular symbols, and noncommutative geometry. They motivate the title of the recent paper by : In [MaMar2](http://www.arxiv.org/abs/hepth/0201036), these and similar results were put in connection with the so called… Read more »

Who was the first mathematician to give a slide show talk? I don’t have the definite answer to this question, but would like to offer a strong candidate : Hermann Minkowski gave the talk “Zur Geometrie der Zahlen” (On the geometry of numbers) before the third ICM in 1904 in Heidelberg and even the title… Read more »

According to a science article in the New York Times, archeologists have discovered “signs of advanced math” in medieval mosaics. An example of a quasicrystalline Penrose pattern was found at the Darbi Imam shrine in Isfahan, Iran. A new study shows that the Islamic patternmaking process, far more intricate than the laying of one‚Äôs bathroom… Read more »

Now that my nongeometry post is linked via the comments in this stringcoffeetable post which in turn is available through a trackback from the KontsevichSoibelman paper it is perhaps useful to add a few links. The little I’ve learned from reading about Connesstyle noncommutative geometry is this : if you have a situation where a… Read more »

Let me admit it : i was probably wrong in this post to advise against downloading A walk in the noncommutative garden by Alain Connes and Matilde Marcolli. After all, it seems that Alain&Matilde are on the verge of proving the biggest open problem in mathematics, the Riemann hypothesis using noncommutative geometry. At least, this… Read more »

A couple of days ago Ars Mathematica had a post Cuntz on noncommutative topology pointing to a (new, for me) paper by Joachim Cuntz A couple of years ago, the Notices of the AMS featured an article on noncommutative geometry a la Connes: Quantum Spaces and Their Noncommutative Topology by Joachim Cuntz. The hallmark of… Read more »

A few days ago, Ars Mathematica wrote : Alain Connes and Mathilde Marcolli have posted a new survey paper on Arxiv A walk in the noncommutative garden. There are many contenders for the title of noncommutative geometry, but Connes‚Äô flavor is the most successful. Be that as it may, do not print this 106 page… Read more »

Are there hidden relations between mathematical and physical constants such as $\frac{e^2}{4 \pi \epsilon_0 h c} \sim \frac{1}{137} $ or are these numerical relations mere accidents? A couple of years ago, Pierre Cartier proposed in his paper A mad day’s work : from Grothendieck to Connes and Kontsevich : the evolution of concepts of space… Read more »
Close