Posts In Category geometry
Lambda-rings for formula-phobics
on February 5, 2010 by lieven in geometry, numbers, Comments (1)
In 1956, Alexander Grothendieck (middle) introduced -rings in an algebraic-geometric context to be commutative rings A equipped with a bunch of operations (for all numbers ) satisfying a list of rather obscure identities. From the easier ones, such as
to those expressing and via specific universal polynomials. An attempt to capture [...]
big Witt vectors for everyone (1/2)
on February 2, 2010 by lieven in geometry, numbers, Comments (1)
Next time you visit your math-library, please have a look whether these books are still on the shelves : Michiel Hazewinkel’s Formal groups and applications, William Fulton’s and Serge Lange’s Riemann-Roch algebra and Donald Knutson’s lambda-rings and the representation theory of the symmetric group.
I wouldn’t be surprised if one or more of these books are [...]
The odd knights of the round table
on January 28, 2010 by lieven in games, geometry, groups, numbers, Comments (0)
Here’s a tiny problem illustrating our limited knowledge of finite fields : “Imagine an infinite queue of Knights , waiting to be seated at the unit-circular table. The master of ceremony (that is, you) must give Knights and a place at an odd root of unity, say and , such that the [...]
Grothendieck’s functor of points
on September 29, 2009 by lieven in geometry, Comments (0)
A comment-thread well worth following while on vacation was Algebraic Geometry without Prime Ideals at the Secret Blogging Seminar. Peter Woit became lyric about it :
My nomination for the all-time highest quality discussion ever held in a blog comment section goes to the comments on this posting at Secret Blogging Seminar, where several of [...]
introducing : the n-geometry cafe
on July 17, 2009 by lieven in general, geometry, iMath, Comments (3)
It all started with this comment on the noncommutative geometry blog by “gabriel” :
Even though my understanding of noncommutative geometry is limited, there are some aspects that I am able to follow. I was wondering, since there are so few blogs here, why don’t you guys forge an alliance with neverending books, you blog about [...]
noncommutative space quiz
on May 21, 2009 by lieven in geometry, lazy blogging, Comments (4)
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 spaces? [...]
Pollock your own noncommutative space
on May 19, 2009 by lieven in geometry, lazy blogging, Comments (4)
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 post) [...]
Views of noncommutative spaces
on May 18, 2009 by lieven in geometry, lazy blogging, Comments (3)
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 geometry [...]
Geometry of the Okubo algebra
on March 14, 2009 by lieven in geometry, groups, Comments (3)
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 [...]
Connes & Consani go categorical
on March 12, 2009 by lieven in geometry, Comments (1)
Today, Alain Connes and Caterina Consani arXived their new paper Schemes over and zeta functions. It is a follow-up to their paper On the notion of geometry over , which I’ve tried to explain in a series of posts starting here.
As Javier noted already last week when they updated their first paper, the [...]
Hi, I'm a professor of mathematics at the University of Antwerp, in Belgium. My research areas are non-commutative algebra and non-commutative geometry. Sometimes, you can also find me here :
