Mathematics Colloquia and Seminars

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Given a pair of smooth manifolds X and Y, topologists must study various classes of smooth mappings between them that satisfy a particular differential property. How can we tell if such a class is generic among all smooth mappings from X to Y? In recent decades, the k-th jet bundle associated with X and Y has proven to be a very valuable tool for addressing this problem. In this talk, I will describe jet bundles, the associated topology on the space of smooth mappings, and two related results that provide a partial answer to this question: the Thom Transversality Theorem and Multijet Transversality Theorem. If time allows, I will discuss some specific applications of these results.