Computing with Affine Algebraic Groups

ARGOMENTI: Seminars Ph.D. Program

Wednesday 25 March 2009 h. 15:00, room 1BC/45
Andrea Pavan (Ph.D. in Pure Math., Dip. Mat.)
"Computing with Affine Algebraic Groups"

How can one solve the Rubik's Cube? The question turns out to be equivalent to a problem about groups, whose solution is provided by Computational Group Theory. More generally, CGT is concerned with designing and analyzing algorithms to compute information about groups which can be described by a finite amount of data. Examples include finite permutation groups, finitely presented groups, finitely generated matrix groups and polycyclic groups, which have been at the center of the subject since the beginning of the last century. On the contrary, very little work has been done on affine algebraic groups. These are, roughly speaking, groups whose elements are solutions to some system of polynomial equations in finitely many indeterminates. Although their structure is well understood, they have been rarely studied from a computational point of view. Two pioneers in the field are Grunewald and Segal, who developed the basis for many useful algorithms.
In the first part of the talk we will give an introductory overview of both Computational Group Theory and the theory of affine algebraic groups. Then we will describe the work of Grunewald and Segal, as well as some improvements of their methods.

Rif. int. C. Marastoni, T. Vargiolu, M. Dalla Riva
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