Mini symposium in honor of Wilberd van der Kallen
January 20th, 2012

Wilberd van der Kallen will turn 65 in January 2012. The Mathematical Institute 
of the University of Utrecht and the Geometry and Quantum Theory cluster will 
celebrate this with a mini symposium in Wilberd's honor on 

January 20, 2012 from 13.00-17.00 hrs. in room 211 of the Minnaert building, de Uithof, Utrecht.

Program: 

13.15-14.15: Prof. Jean Fasel (Mathematisches Institut der Universität München) 
Unimodular rows 

14.15-14.45: Coffee and tea

14.45-15.45: Prof. Henning Haahr Andersen (Department of Mathematics, University of Aarhus) 
Tilting modules for reductive algebraic groups

16.00-17.00: Prof. Antoine Touzé (Institut Galilée, Université Paris 13) 
Frobenius twists in higher invariant theory 

17.00-18.30: drinks in the library of the Math building

Afterwards (19.30- ) there is a dinner in the Academiegebouw of the University of Utrecht. 
If you want to join (approx. 50 euro), please send an e-mail (also indicate if you have 
diet restrictions or if you want a vegetarian dinner) to both Jan Stienstra and 
Johan van de Leur (J.Stienstra@uu.nl and J.W.vandeLeur@uu.nl) before Thursday January 5.

Abstracts: 

Jean Fasel, Unimodular rows Let R be a commutative noetherian
ring. A projective R-module P is said to be stably free if P⊕Rn≅Rm. By
induction, the study of such modules reduces to the case P⊕R≅Rs. Such
modules correspond to what is called unimodular rows of rank n. We will
survey W. van der Kallen's work on such rows and then present some recent
developments in the subject.

Henning Haahr Andersen, Tilting modules for reductive algebraic groups
Let G be a reductive algebraic group over a field k, e.g. G = GLn(k). In
this talk we shall describe the indecomposable tilting modules for G
and discuss some of their properties. We will also point to some open
problems in representation theory.

Antoine Touzé, Frobenius twists in higher invariant theory Let V be a
representation of the algebraic group GLn(k). If k is a field of positive
characteristic, one can use the Frobenius isomorphism of x→xp to form
a twisted representation V(1) of GLn(k). Such representations naturally
appear in many problems from representation theory. In this talk we will
explain two results where such representations play a crucial role. First
they appear in the proof of van der Kallen's conjecture (now a theorem
Touzé, van der Kallen) that reductive algebraic groups have finitely
generated cohomology algebras. Second, extensions between such twisted
representations also control the cohomology of finite Lie groups (this
is a theorem by Cline, Parshall, Scott and van der Kallen). Then we will
give some very recent results on the cohomological behaviour of these
twisted representations.