Seminar talk, 19 October 2011: Difference between revisions
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| speaker = Pavel Bibikov | | speaker = Pavel Bibikov | ||
| title = On differential invariants of G-manifolds | | title = On differential invariants of G-manifolds | ||
| abstract = Consider an action of a group G on a manifold M. This action prolongs to action on the space of functions on M. The talk will discuss a new method of construction the field of differential invariants of this action (and, as a consequence, classification of G-orbits of functions on M). | | abstract = Consider an action of a group <math>G</math> on a manifold <math>M</math>. This action prolongs to action on the space of functions on <math>M</math>. The talk will discuss a new method of construction the field of differential invariants of this action (and, as a consequence, classification of <math>G</math>-orbits of functions on <math>M</math>). | ||
As an example, there will be discussed solutions of the problems of classification \mathrm{GL}_3(\mathbb{C})- and \mathrm{SO}_3(\mathbb{C})-orbits of ternary forms. Then there will be considered a solution of more general problem of classification of G-orbit of homogeneous form in many variables. Surprisingly, this classification does not depend on the degree of the form, on the number of variables, and even on (in a sense) the group G. | As an example, there will be discussed solutions of the problems of classification <math>\mathrm{GL}_3(\mathbb{C})</math>- and <math>\mathrm{SO}_3(\mathbb{C})</math>-orbits of ternary forms. Then there will be considered a solution of more general problem of classification of <math>G</math>-orbit of homogeneous form in many variables. Surprisingly, this classification does not depend on the degree of the form, on the number of variables, and even on (in a sense) the group <math>G</math>. | ||
In conclusion, there will be explained how to generalized these results to classification of G-orbit of functions on manifolds. | In conclusion, there will be explained how to generalized these results to classification of <math>G</math>-orbit of functions on manifolds. | ||
| slides = | | slides = | ||
| references = | | references = | ||
| 79YY-MM-DD = 7988-89-80 | | 79YY-MM-DD = 7988-89-80 | ||
}} | }} | ||
Revision as of 23:47, 7 October 2011
Speaker: Pavel Bibikov
Title: On differential invariants of G-manifolds
Abstract:
Consider an action of a group on a manifold . This action prolongs to action on the space of functions on . The talk will discuss a new method of construction the field of differential invariants of this action (and, as a consequence, classification of -orbits of functions on ).
As an example, there will be discussed solutions of the problems of classification - and -orbits of ternary forms. Then there will be considered a solution of more general problem of classification of -orbit of homogeneous form in many variables. Surprisingly, this classification does not depend on the degree of the form, on the number of variables, and even on (in a sense) the group .
In conclusion, there will be explained how to generalized these results to classification of -orbit of functions on manifolds.