Vladimir Popov, Moscow State Technical University
1. Brief historical overview
2. Biregular Invariant Theory
Generators and relations. Hilbert's 14th problem. Constructive Invariant Theory: explicit bounds. Good properties in Invariant Theory, three sources: Commutative Algebra, Algebraic Geometry, Representation Theory. Finiteness theorems. Explicit classifications of actions with good properties.
3. Birational Invariant Theory
Birational classification of actions. Essential dimension of algebraic groups and Hilbert's 13th problem.
| [1] | V. L. Popov, E. B. Vinberg, Invariant Theory, Encycl. of Math. Sci., Algebraic Geometry. IV, Springer Verlag, Vol. 55, 1994, 123-284. |
| [2] | Z. Reichstein, On the notion of essential dimension for algebraic groups, Transformation Groups 5 (2000), No. 3, 265-304. |
| [3] | H. Derksen, G. Kemper, Computational Invariant Theory, forthcoming: Springer Verlag, 2002. |
| E-Mail: | popov@ppc.msk.ru |