Cel Research activities are related to the following topics.Jacobian Conjecture for polynomial morphisms of affine spaces;Algebraic group actions on affine space.Dual varieties of orbits and generalised discriminants;Standard monomial theory and geometry of Schubert varieties;Constructive methods for invariant theory and representations;Quantum groups with applying methods of algebraic transformation groups;Representation and invariant theories of some remarkable classes of linear actions, and applications;Algebraic geometric properties of algebraic group actions.Objectives and expected results:1. Investigating two representation theoretic approaches to the Jacobian Conjecture and related problems with a view towards proving Mathieu conjecture (at least for some groups) and the corresponding identity for the covariants;2. Investigating nonreductive algebraic group actions on affine space with a view towards finding answers (presumably, negative) to the basic problems (e.g. cancellation problem);3. Describing dual varieties of a class of orbits of linear actions and developing a generalization of the theory of discriminants of linear bundles over flag varieties;4. Investigating some problems related to the general construction of a standard monomial theory for Schubert varieties and involved quantum groups at root of unity, with application to constructing deformations of Schubert varieties for all simple groups;5. Developing methods of constructive Invariant theory with a view towards finding the improved general degree bounds, the relevant computer algorithms and implementations, and the specific explicit descriptions for binary forms, cyclic and symmetric groups;6. Obtaining a canonical presentation by generators and relations for the affine coordinate algebra of a connected reductive algebraic group with a view towards finding its quantization in arbitrary characteristic;7. Developing "quantized shuffle approach" to quantized Kac-Moody algebras and constructing PBW type bases for finite dimensional enveloping algebras at root of unity;8. Investigating orbits and some problems of harmonic analysis for dual pairs, certain classes of prehomogeneous vector spaces, and gradings of Lie algebras;9. Finding new stability criteria for some nonlinear actions;10. Obtaining the combinatorial counterparts of the basic algebraic geometric properties for some natural classes of algebraic transformation spaces;11. Classifying linear actions of connected simple algebraic groups such that the algebra of invariants is a complete intersection;12. Proving equality of essential dimensions of an algebraic group and its Levi subgroup. Program(-y) IC-INTAS - International Association for the promotion of cooperation with scientists from the independent states of the former Soviet Union (INTAS), 1993- Temat(-y) 2 - Mathematics, Telecommunications, Information Technologies INTAS - INTAS Zaproszenie do składania wniosków Data not available System finansowania Data not available Koordynator University of Basel Wkład UE Brak danych Adres Rheinsprung, 21 4051 Basel Szwajcaria Zobacz na mapie Koszt całkowity Brak danych Uczestnicy (4) Sortuj alfabetycznie Sortuj według wkładu UE Rozwiń wszystko Zwiń wszystko M.V. Lomonosov Moscow State University Rosja Wkład UE Brak danych Adres Vorob'evy Gory 119899 Moscow Zobacz na mapie Koszt całkowity Brak danych Moscow State Technical University MGIEM Rosja Wkład UE Brak danych Adres Bol'shoi Trekhsvyatitel'skii per, 3/12 109028 Moscow Zobacz na mapie Koszt całkowity Brak danych Tbilisi Mathematical Institute Gruzja Wkład UE Brak danych Adres ul. Meraba Alexidze, 1 380093 Tbilisi Zobacz na mapie Koszt całkowity Brak danych Universite Louis Pasteur Francja Wkład UE Brak danych Adres rue Rene Descartes, 7 67084 Strasbourg Zobacz na mapie Koszt całkowity Brak danych
