Classical spectral asymptotics with a modern twist

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• Leonid Parnovski (University College London)
• Tuesday 13 January 2026, 10:15-11:15
• Seminar Room 1, Newton Institute.

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GSTW01 - High energy spectral theory: geometry and dynamics

The existence of spectral asymptotics of Laplace or Schroedinger operators acting on Riemannian manifolds is a classical problem studied for more than 100 years. It has been 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 resent progress: proving this conjecture in special cases, as well as constructing some counterexamples. Some of the results will be new even for people who have heard an earlier version of this talk. This is a joint work with Jeff Galkowski (UCL) and Roman Shterenberg (UAB)

This talk is part of the Isaac Newton Institute Seminar Series series.

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