Title: Some mathematical aspects of Rubik's cube
Speaker: Wilberd van der Kallen (Utrech University)
Abstract: This talk is more accessible than most other colloquium talks by this speaker. First it is explained why there are only 43252003274489856000 configurations of the cube. Next some principles are discussed that allow you to design your own library of routines to solve the cube.
Bio Sketch: Wilberd van der Kallen is a mathematician from Utrecht University, The Netherlands. He studied algebraic groups under T. A. Springer. After defending his thesis in 1973 he got interested in algebraic K-theory, in particular stabilization issues. His strangest result in this area is a group structure on certain orbit sets of unimodular rows, analogous to the cohomotopy groups of Borsuk in algebraic topology. Gradually his work shifted back to representation theory of algebraic groups. Here the Frobenius map keeps turning up. (Frobenius twist of a representation, Frobenius splitting of a variety, ..) He conjectured a deep connection between classical invariant theory and the cohomology of representations of linear algebraic groups. This conjecture was confirmed by Antoine Touzé in 2008 and Wilberd is still trying to understand the proof better.