BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Eigenvalue and heat trace asymptotics for drifting Laplacians Rowlett, Julie


This talk is based on joint work with Nelia Charalambous, in which we consider the spectra of drifting (aka weighted or Bakry-Émery) Laplace operators on Riemannian manifolds. We shall discuss eigenvalue estimates and Weyl's law in this setting. The proof of Weyl's law is via the short time asymptotic expansion of the heat trace, and so we will discuss this expansion. In this work, we assume only finite regularity of the weight function, and we shall see that the behavior of the short time asymptotics of the heat trace determines, and conversely is determined by the regularity of the weight function.

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