SEMINAR.....
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Speaker |
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Prof Ravi. S. Kulkarni
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Affiliation |
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Harish Chandra Research Institute
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Subject Area |
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Mathematics
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Venue |
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Lecture Hall I, Dept of Mathematics
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Time |
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4.00 pm
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Date |
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September 12, 2005
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Event Title1 |
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"Dynamical Types of Transformations in Classical Geometries"
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| Abstract |
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| In all classical geometries, for example, Euclidean, spherical,hyperbolic, linear, affine, projective, inversive,... also their complex and quaternionic analogues, we talk about "dynamical types" of transformations, and observe that in each case there are only finitely many "dynamical types". There is no general definition of a "dynamical types" in the literature. In this lecture, we shall offer a definition of a "dynamical type", and account for the finiteness phenomenon. We shall observe that the underlying field of real numbers in the examples cited above plays a crucial role. If we define the anologues of the above-cited geometries over other fields, we observe that the "finiteness of dynamical types" no longer holds. There arise new arithmetic invariants. e results are obtained from some very general results on arbitrary group actions, which can serve to unify certain parts of mathematics. As an example we cite the theory of Rational Canonical Forms of n x n matrices, and the Frobenius' theory of Centralizers of such matrices. | ||