
books, geometry, noncommutative, representations
let’s spend 3K on (math)books
Posted on by lievenlbSanta gave me 3000 Euros to spend on books. One downside: I have to give him my wishlist before monday. So, I’d better get started. Clearly, any further suggestions you might have will be much appreciated, either in the comments below or more directly via email. Today I’ll focus on my own interests: algebraic geometry,… Read more »

Supernatural numbers also appear in noncommutative geometry via James Glimm’s characterisation of a class of simple $C^*$algebras, the UHFalgebras. A uniformly hyperfine (or, UHF) algebra $A$ is a $C^*$algebra that can be written as the closure, in the norm topology, of an increasing union of finitedimensional full matrix algebras $M_{c_1}(\mathbb{C}) \subset M_{c_2}(\mathbb{C}) \subset … \quad… Read more »

A standard Grassmannian $Gr(m,V)$ is the manifold having as its points all possible $m$dimensional subspaces of a given vectorspace $V$. As an example, $Gr(1,V)$ is the set of lines through the origin in $V$ and therefore is the projective space $\mathbb{P}(V)$. Grassmannians are among the nicest projective varieties, they are smooth and allow a cell… Read more »

This week i was at the conference Noncommutative Algebraic Geometry and its Applications to Physics at the Lorentz center in Leiden. It was refreshing to go to a conference where i knew only a handful of people beforehand and where everything was organized to Oberwolfach perfection. Perhaps i’ll post someday on some of the (to… Read more »

Almost three decades ago, Yuri Manin submitted the paper “New dimensions in geometry” to the 25th Arbeitstagung, Bonn 1984. It is published in its proceedings, Springer Lecture Notes in Mathematics 1111, 59101 and there’s a review of the paper available online in the Bulletin of the AMS written by Daniel Burns. In the introduction Manin… Read more »

I’ve never apologized for prolonged periods of blogsilence and have no intention to start now. But, sometimes you need to expose the things holding you back before you can turn the page and (hopefully) start afresh. Long time readers of this blog know I’ve often warned against groupthink, personality cults and the making of exaggerate… Read more »

Here are the scans of my crude prepnotes for some of the later seminartalks. These notes still contain mistakes, most of them were corrected during the talks. So, please, read these notes with both mercy are caution! Hurwitz formula imples ABC : The proof of Smirnov’s argument, but modified so that one doesn’t require an… Read more »

F_un Mathematics Hardly a ‘new’ blog, but one that is getting a new life! On its old homepage you’ll find a diagonal banner stating ‘This site has moved’ and clicking on it will guide you to its new location : cage.ugent.be/~kthas/Fun. From now on, this site will be hosted at the University of Ghent and… Read more »

Penrose tilings are aperiodic tilings of the plane, made from 2 sort of tiles : kites and darts. It is well known (see for example the standard textbook tilings and patterns section 10.5) that one can describe a Penrose tiling around a given point in the plane as an infinite sequence of 0’s and 1’s,… Read more »

The lecturers, topics and dates of the 6 minicourses in our ‘advanced master degree 2011 in noncommutative algebra and geometry’ are : February 2125 Vladimir Bavula (University of Sheffield) : Localization Theory of Rings and Modules March 711 HansJürgen Schneider (University of München) : Nichols Algebra and Root Systems April 1112 Bernhard Keller (Université Paris… Read more »

Guest post by Fred Van Oystaeyen. In my book “Virtual Topology and Functorial Geometry” (Taylor and Francis, 2009) I proposed a noncommutative version of spacetime ; it is a toy model, but mathematically correct and I included a few philosophical remarks about : “What if reality is noncommutative ?”. I want to add a few… Read more »

The odd Knight of the round table problem asks for a consistent placement of the nth Knight in the row at an odd root of unity, compatible with the two different realizations of the algebraic closure of the field with two elements. The first identifies the multiplicative group of its nonzero elements with the group… Read more »

noncommutative, web
Jason & David, the Ninja warriors of noncommutative geometry
Posted on by lievenlbSocialMention gives a rather accurate picture of the webbuzz on a specific topic. For this reason I check it irregularly to know what’s going on in noncommutative geometry, at least webwise. Yesterday, I noticed two new kids on the block : Jason and David. Their blogs have (so far ) 44 resp. 27 posts, this… Read more »

Never a dull moment with Books Ngram Viewer. Pick your favorite topic(s) and try to explain and name valleys and peaks in the Ngram. An example. I wanted to compare the relative impact of a couple of topics I love, algebraic geometry (blue), category theory (red), representation theory (green) and noncommutative geometry (the bit of… 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 »

Creating (or taking) an image and explaining how it depicts your mental picture of a noncommutative space is one thing. Ideally, the image should be strong enough so that other people familiar with it might have a reasonable guess what you attempt to depict. But, is there already enough concordance in our views of noncommutative… Read more »

Today, Alain Connes and Caterina Consani arXived their new paper Schemes over $ \mathbb{F}_1$ and zeta functions. It is a followup to their paper On the notion of geometry over $ \mathbb{F}_1$, which I’ve tried to explain in a series of posts starting here. As Javier noted already last week when they updated their first… Read more »

We use Kontsevich’s idea of thin varieties to define complexified varieties over F\_un.

We propose to extend the ConnesConsani definition to noncommuntative F_un varieties.

Thanks for clicking through… I guess. If nothing else, it shows that just as much as the stock market is fueled by greed, mathematical reasearch is driven by frustration (or the pleasure gained from knowing others to be frustrated). I did spend the better part of the day doing a lengthy, if not laborious, calculation,… Read more »
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