Almost Sure Weyl Law for Toeplitz Operators

The HADES seminar on Tuesday, February 8 will be at 3:30 pm in Room 740.

Speaker: Izak Oltman

Abstract: When computing eigenvalues of finite-rank non-self-adjoint operators, significant numerical inaccuracies often occur when the rank of the operator is sufficiently large. I show the spectrum of Toeplitz operators, with a random perturbation added, satisfy a Weyl law with probability close to one. I will begin with numerical animations, demonstrating this result for quantizations of the torus (a result proven by Martin Vogel in 2020). Then give a brief introduction to Toeplitz operator (quantizations of functions on Kahler Manifolds). And finally outline the main parts of the proof, which involve constructing an `exotic calculus’ of symbols on a Kahler manifold.

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