Title: Derivations on Operator Algebras and Quantum Dynamics
Speaker: Shavkat Ayupov
Institution: V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences
Date & Time: September 21, 2024, 8:30–9:30
Location: Room 209, Zhengxin Building, Jilin University
This talk provides a complete resolution to the problem posed by Ayupov in 2000 (and partially restated in 2014 by Kadison and Liu) concerning derivations on algebras of measurable operators affiliated with von Neumann algebras. First, we review preliminaries from operator algebra theory and non-commutative integration, highlighting the physical motivations for automorphisms and derivations in operator algebras. The second part discusses the background of the Ayupov-Kadison-Liu Problem and its connections to classical derivation theory in operator algebras, tracing back to foundational work by Kaplanski, Kadison, Sakai, and others. We will cite and briefly explain key results on derivations in algebras of unbounded operators, survey special cases of the problem, and finally state the main theorem yielding its full resolution.
Shavkat Ayupov is the Director of the V.I. Romanovskiy Institute of Mathematics at the Uzbekistan Academy of Sciences. His research focuses on operator algebra theory, quantum probability, and the structure theory of non-associative algebras (Jordan, Lie, Leibniz, etc.). He is the author of multiple monographs on real and Jordan structures in operator algebras and the structure theory of Leibniz algebras.
A member of the Uzbekistan Academy of Sciences since 1995, he is also a Fellow of TWAS (The World Academy of Sciences, 2003), a Senior Associate of ICTP (International Centre for Theoretical Physics, 2008–2013), and a Guest Professor at Sichuan University (Chengdu, China, 2015–2021). He serves as the Managing Editor of the
Uzbek Mathematical Journal and an editor of
Advances in Operator Theory. In 2017, he received the First-Class State Prize in Science and Technology of the Republic of Uzbekistan.
