Tuesday, October 07 | |
Analysis Seminar
Time: 14:30
Speaker: Ilya Kossovskiy (University of Vienna) Title: "Dynamical Approach in CR-geometry and Applications" Room: MC 107 Abstract: Study of equivalences and symmetries of real submanifolds in complex space goes back to the classical work of Poincare and Cartan and was deeply developed in later work of Tanaka and Chern and Moser. This work initiated far going research in the area (since 1970's till present), which is dedicated to questions of regularity of mappings between real submanifolds in complex space, unique jet determination of mappings, solution of the equivalence problem, and study of automorphism groups of real submanifolds. Current state of the art and methods involved provide satisfactory (and sometimes complete) solution for the above mentioned problems in nondegenerate settings. However, very little is known for more degenerate situations, i.e., when real submanifolds under consideration admit certain singularities of the CR-structure (such as non-constancy of the CR-dimension or that of the CR-orbit dimension). The recent CR (Cauchey-Riemann Manifolds) -- DS (Dynamical Systems) technique, developed in our joint work with Shafikov and Lamel, suggests to replace a real submanifold with a CR-singularity by appropriate complex dynamical systems. This technique has recently hepled to solve a number of long-standing problems in CR-geometry, related to regularity of CR-mappings. In this talk, we give an overview of the technique and the results obtained recently by using it. We also discuss a possible development in this direction, in particular, new sectorial extension phenomena for CR-mappings. | |
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the University of Western Ontario
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