We shall initially discuss what symmetries mean in the context of dynamical systems of different flavors: complex analytic, Hamiltonian, or smooth. We shall then discuss progress towards a resolution of a conjecture of Smale: a generic smooth dynamical system has only trivial symmetries.
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This colloquium is part of the Distinguished Lecture Series (DLS) organized by The (Indian) Mathematics Consortium (TMC), and co-hosted by IIT-B and ICTS-TIFR. For more information about this lecture series, and to register, please visit the homepage of the TMC DLS.