Speaker: Konstantinos Efstathiou (Duke Kunshan)
Time: 2025-11-07 14:00-15:00
Location: 1710, SIMIS
Zoom Meeting ID:844 0594 7424 Passcode:076895
Abstract: The problem of the classification of finite-dimensional integrable Hamiltonian systems has been intensely studied in the past few decades. While the typical fibre of an integrable Hamiltonian system is a torus, and the Arnold-Liouville theorem asserts that the nearby fibration is trivial, the existence of singular fibers complicates the global geometry and the attempts for classification. Seminal results in this direction include the classification of toric systems by Delzant, and the classification of semitoric systems by Vũ Ngọc and Pelayo. However, large classes of integrable Hamiltonian systems have yet to be classified. In this talk we will discuss the problem of classification, while focusing on certain topological invariants, monodromy and fractional monodromy, and how to compute them in systems with a complexity-1 torus action. Moreover, we will explore the connection between these invariants, classification, and the structure of the joint spectrum for the corresponding quantum integrable systems. Finally, we will consider the extension of these concepts to systems with non-compact fibers.
About Speaker: Professor Konstantinis Efstathiou is an Associate Professor of Mathematics at Duke Kunshan University, studying the intersections between Mathematical Physics and Dynamical Systems – in particular, he is an expert on the geometry of integrable Hamiltonian systems, and the dynamics of coupled oscillator networks. He is currently serving as the DKU co-director of the Zu Chongzhi Center for Mathematics and Computational Sciences. He received his BSc and MSc in Physics from the University of Athens, Greece, and his PhD in Physics from the Université Littoral Côte d’Opale, France, in 2004. After a postdoc at the University of Groningen, he worked as Lecturer at the Xi’an Jiaotong Liverpool University in Suzhou, China, where he also served as acting Head of Department. He has published a research monograph in the prestigious Springer Lecture Notes in Mathematics and several papers in top journals in his field, including Reviews of Modern Physics, Physical Review Letters, and Communications in Mathematical Physics.
简体中文 
English