BZ Seminar in Analysis: Leonid Parnovski (London)

Classical spectral asymptotics with a modern twist

The existence of spectral asymptotics of Laplace or Schroedinger operators acting on Riemannian manifolds is a classical problem known for more than 100 years. It has ben known for a long time that obstacles to the existence of spectral asymptotic expansions are periodic and looping trajectories of the geodesic flow. A conjecture formulated in 2016 stated that these trajectories are the only such obstacles. I will discuss the history of this problem and describe the recent progress: proving this conjecture in special cases, as well as constructing some counterexamples.

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