Posts In Category numbers
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 [...]
On2 : extending Lenstra’s list
on January 27, 2009 by lieven in games, numbers, Comments (0)
Hendrik Lenstra found an effective procedure to compute the mysterious elements alpha(p) needed to do actual calculations with infinite nim-arithmetic.
On2 : Conway’s nim-arithmetics
on January 26, 2009 by lieven in games, numbers, Comments (0)
Conway’s nim-arithmetic on ordinal numbers leads to many surprising identities, for example who would have thought that the third power of the first infinite ordinal equals 2…
On2 : transfinite number hacking
on January 8, 2009 by lieven in games, numbers, Comments (1)
Surely Georg Cantor’s transfinite ordinal numbers do not have a real-life importance? Well, think again.
Dedekind or Klein ?
on April 22, 2008 by lieven in groups, modular, numbers, Comments (3)
The black&white psychedelic picture on the left of a tessellation of the hyperbolic upper-halfplane, was called the Dedekind tessellation in this post, following the reference given by John Stillwell in his excellent paper Modular Miracles, The American Mathematical Monthly, 108 (2001) 70-76.
But is this correct terminology? Nobody else uses it apparently. So, let’s [...]
Surreal numbers & chess
on April 8, 2008 by lieven in games, numbers, Comments (2)
Most chess programs are able to give a numerical evaluation of a position. For example, the position below is considered to be worth +8.7 with white to move, and, -0.7 with black to move (by a certain program). But, if one applies combinatorial game theory as in John Conway’s ONAG and the Berlekamp-Conway-Guy masterpiece Winning [...]
the secret revealed…
on March 26, 2008 by lieven in groups, modular, numbers, Comments (3)
Often, one can appreciate the answer to a problem only after having spend some time trying to solve it, and having failed … pathetically.
When someone with a track-record of coming up with surprising mathematical tidbits like John McKay sends me a mystery message claiming to contain “The secret of Monstrous Moonshine and the universe”, I’m [...]
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 :
