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 [...]

Read more...

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 [...]

Read more...

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 [...]

Read more...

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 [...]

Read more...

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 [...]

Read more...

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? [...]

Read more...

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) [...]

Read more...

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 [...]

Read more...

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 [...]

Read more...

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 [...]

Read more...