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Lecture on "Ruelle–Pollicott Resonances of Atochastic Systems and a New Approach to Stochastic Bifurcations"
Date and Time: 2020-06-10 11:48:35

Speaker: Mickaël D. Chekroun, Doctor, Weizmann Institute of Science & UCLA

Date: June 11, 2020

Time: 4:30 p.m.

Location: 119 Lecture Hall, Huagangyuan East Building, Qingdao Campus

Joining Zoom Meeting: ID 159 801 0503

Sponsor: Research Center for Mathematics and Interdisciplinary Sciences


In this talk, a theory of Ruelle-Pollicott(RP) resonances for systems of stochastic differential equations(SDEs) will be presented, valid for a broad class of stochastic systems. Roughly speaking, RP resonances are defined, in the stochastic context, as the eigenvalues of the generator (Kolmogorov operator) of a given stochastic system. By relying on the theory of Markov semigroups and the spectral theory of semigroups, decomposition formulas of correlation functions and power spectral densities( PSDs) in terms of RP resonances will be then presented (Chekroun et al., 2020)

By extending the results of (Chekroun et al., 2014), it will be explained how a notion of reduced RP resonances can be rigorously framed, as soon as the dynamics is partially observed within a reduced state space V. Applications to the detection and characterization of such stochastic nonlinear oscillations in a high-dimensional stochastic system, namely the Cane-Zebiak model of EL Niño-Southern Oscillation (ENSO) (Cao et al., 2019) subject to noise modeling fast atmospheric fluctuations, will be finally discussed.


The work of Dr. Chekroun is at the confluence zone between the theory of stochastic/nonlinear dynamics and functional analysis (semigroup theory). his work at the interface of Mathematics and climate science has been crowned by the several grants awarded by major US governmental agencies including the Department of the National Science Foundation (NSF), the Machine Learning, Reasoning and Intelligence program of the Office of Naval Research (ONR), and the Applied and Computational Analysis program of the ONR.

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Edited by: Su Chang, Xie Tingting

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