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Topics in Complex and Real Geometry

On the trajectories of gradient vector fields

speaker: Adam Parusinski (Université d'Angers - Département de Mathématiques)

abstract: We present the proof of the gradient conjecture of R. Thom of Kurdyka, Mostowski, Parusinski, Ann. Math. 152 (2000). The conjecture states that the integral curves of the gradient of $f$, where $f$ is a real analytic function on an open subset of $R^n$, admit tangent lines at their limit points. The proof of conjecture is based on the theory of singularities. We discuss also the existence of analytic trajectories and the o-minimal case.

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