Seminario di equazioni differenziali e applicazioni: “Kolmogorov-Fokker-Planck operators in dimension two: heat kernel and curvature”

Mercoledì 13 Marzo 2019, ore 12:00 - Aula 1BC45 - Francesco Boarotto


Mercoledì 13 Marzo 2019 alle ore 12:00 in Aula 1BC45, Francesco Boarotto (Università di Padova) terrà un seminario dal titolo “Kolmogorov-Fokker-Planck operators in dimension two: heat kernel and curvature”.

We consider the heat equation associated with a class of hypoelliptic operators of Kolmogorov-Fokker-Planck type in dimension two. We explicitly compute the first meaningful coefficient of the small time asymptotic expansion of the heat kernel on the diagonal, and we interpret it in terms of curvature-like invariants of the optimal control problem associated with the diffusion. This gives a first example of geometric interpretation of the small-time heat kernel asymptotics of non-homogeneous Hormander operators which are not associated with a sub-Riemannian structure, i.e., whose second-order part does not satisfy the Hormander condition. If time permits, we will discuss a slightly more complicated example where answers are not so clear. Joint work with D. Barilari.

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