Tag: geometry

  • Bourbakism & the queen bee syndrome

    Probably the smartest move I’ve made after entering math-school was to fall in love with a feminist. Yeah well, perhaps I’ll expand a bit on this sentence another time. For now, suffice it to say that I did pick up a few words in the process, among them : the queen bee syndrome : women […]

  • Now here’s an idea

    Boy, do I feel stupid for having written close to 500 blog-posts hoping (in vain) they might eventually converge into a book project… Gil Kalai is infinitely smarter. Get a fake gmail account, invent a fictitious character and start COMMENTING and provoking responses. That’s how “Gina” appeared on the scene, cut and pasted her comments…

  • Pollock your own noncommutative space

    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…

  • Views of noncommutative spaces

    The general public expects pictures from geometers, even from non-commutative 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…

  • The Scottish solids hoax

    A truly good math-story gets spread rather than scrutinized. And a good story it was : more than a millenium before Plato, the Neolithic Scottish Math Society classified the five regular solids : tetrahedron, cube, octahedron, dodecahedron and icosahedron. And, we had solid evidence to support this claim : the NSMS mass-produced stone replicas of…

  • Geometry of the Okubo algebra

    Last week, Melanie Raczek gave a talk entitled ‘Cubic forms and Okubo product’ in our Artseminar, based on her paper On ternary cubic forms that determine central simple algebras of degree 3. I had never heard of this strange non-associative product on 8-dimensional space, but I guess it is an instance of synchronicity that now…

  • Connes & Consani go categorical

    Today, Alain Connes and Caterina Consani arXived their new paper Schemes over $ \mathbb{F}_1$ and zeta functions. It is a follow-up 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…

  • On2 : transfinite number hacking

    Surely Georg Cantor’s transfinite ordinal numbers do not have a real-life importance? Well, think again.

  • Manin’s geometric axis

    Manin proposes the idea of projecting spec(Z[x]) not only onto spec(Z), but also to a geometric axis by considering the integers as an algebra over the field with one element.

  • Mumford’s treasure map

    In the series “Brave new geometries” we give an introduction to ‘strange’ but exciting new ideas. We start with Grothendieck’s scheme-revolution, go on with Soule’s geometry over the field with one element, Mazur’s arithmetic topology, Grothendieck’s anabelian geometry, Connes’ noncommutative geometry etc.