Speaker: Yulin Gong (Tsinghua University)
Host: Xiaolong Hans Han
Abstract: We study the spectral distribution of damped waves on compact negatively curved manifolds. Sjöstrand proved that the imaginary parts of the majority of the eigenvalues concentrate near the average of the damping function, see also in Anantharaman’s paper. In this paper, we prove that the most of eigenvalues actually lie in certain regions with imaginary parts that approach the average logarithmically as the real parts tend to infinity. The proof relies on the moderate deviation principles for Anosov geodesic flows. As an application, we show the concentration of non-trivial zeros of twisted Selberg zeta functions in a logarithmic region asymptotically close to Re s=1/2.
Time: Wednesday 10 am, 02/19
Location: Simis 1510
About the speaker: Yulin Gong is currently a graduate student at Tsinghua Univerisity, supervised by Prof. Long Jin. He is interested in microlocal analysis, spectral geometry, dynamical systems, and random surfaces and graphs. His current research is on the spectral distribution of a type of non-self-adjoint operators on compact negatively curved manifolds.
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