Abstract
Many physical systems can be described using evolution of states. Observations are then based on correlations: the speaker measures the time evolved state against another state. The time representation can be replaced by the frequency representation (by taking a Fourier transform) which produces the power spectrum. Riemann first proposed, in a different language, that fine features of correlations can be understood by continuing the power spectrum into complex frequencies.
The speaker will explain recent progress in the study of these concepts in the setting of chaotic dynamics. In that case the analytic continuation of the power spectrum is related to the continuation of Selberg, Smale and Ruelle zeta functions which are analogues of the Riemann zeta function for dynamical systems.
About the speaker
Prof Maciej Zworski received PhD in Mathematics from Massachusetts Institute of Technology in 1989, and was Assistant Professor there until 1992. He had been faculty at Johns Hopkins University and the University of Toronto. He joined the University of California at Berkeley in 1998, and is currently Professor of Mathematics.
Prof Zworski’s research interests include microlocal analysis, scattering theory, and partial differential equations. He is editor of the journals including Analysis & PDE, American Journal of Mathematics, Applied Mathematics Research eXpress and Methods and Applications of Analysis, etc.
Prof Zworski received awards including the Coxeter-James Prize from the Canadian Mathematical Society and Jon A. Bucsela Prize in Mathematics. He is a Fellow of the Royal Society of Canada and the American Academy of Arts and Sciences.
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