Department of Mathematics colloquium - Sibe Mardešić presents a sequence of lectures given by leading experts in the fields of theoretical and applied mathematics. The lectures take place at the Department of Mathematics, Faculty of Science, Bijenička cesta 30, Zagreb.
Lecture announcement
About the lecturer: Professor Mezic works in the field dynamical systems, control theory and applications in artificial intelligence. He did his Ph. D. in Dynamical Systems at the California Institute of Technology. Dr. Mezic was a postdoctoral researcher at the Mathematics Institute, University of Warwick, UK in 1994-95. From 1995 to 1999 he was a member of College of Engineering at the University of California, Santa Barbara where he is currently a Distinguished Professor. In 2000-2001 he has worked as an Associate Professor at Harvard University in the Division of Engineering and Applied Sciences. He won the Alfred P. Sloan Fellowship in Mathematics, NSF CAREER Award from the National Science Foundation and the George S. Axelby Outstanding Paper Award from IEEE. He also won the United Technologies Senior Vice President for Science and Technology Special Achievement Prize in 2007. For his work on analysis and control of complex systems, he was named Fellow of the American Physical Society, Fellow of the Society for Industrial and Applied Mathematics and Fellow of the Institute of Electrical and Electronics Engineers. He is the recipient of the 2021 J. D. Crawford SIAM Prize, awarded once in two years to a researcher in Dynamical Systems.
Lecture abstract: The Koopman operator, invented in 1931, initially provided a rich framework for ergodic theory, a part of dynamical systems that aims to describe their statistical properties. Its connections with nonequilibrium statistical mechanics made it a useful tool in physics and chemistry. In recent years, its use in machine learning is becoming widespread. I will discuss its mathematical underpinnings with an emphasis on functional space constructions. The interplay of spectral reduction theory and geometrical dynamical systems theory yields a fascinating merger of concepts from two seemingly disparate mathematical fields that will be described. I will also present the associated applications and extensions that made Koopman operator theory an essential tool in modern AI. Literature: Mezić, I., 2021. Koopman operator, geometry, and learning of dynamical systems. Not. Am. Math. Soc, 68(7), pp.1087-1105. Acknowledgement: Support from ARO, AFOSR, DARPA, NSF and ONR is gratefully acknowledged.