Dual Lyapunov Exponents and Global Theory of Analytic Quasiperiodic Operators: the Robustness of Sharp Spectral Results
Time: 2026-01-08
Published By: Ruixin Li
Speaker(s): Svetlana Jitomirskaya (UC Berkeley)
Time: 16:00-17:00 January 13, 2026
Venue: Room 77201, Jingchunyuan 78, BICMR
Abstract:
We will briefly review the main concepts and fascinating physics background of one-dimensional analytic quasiperiodic operators and their associated cocycles. We will then present highlights of our joint work with Lingrui Ge, Jiangong You, and Qi Zhou on a non-commutative generalization of Jensen’s formula, and explain how it uncovers the mystery behind Avila’s global theory. Then, we will discuss the work of Ge and our joint work with Ge and with Ge and You, showing how the duality approach helps prove previously model-specific sharp spectral statements in a robust way. The talk is intended for a broad mathematical audience, with emphasis on ideas and mechanisms rather than technical details.
Bio-Sketch:
We will briefly review the main concepts and fascinating physics background of one-dimensional analytic quasiperiodic operators and their associated cocycles. We will then present highlights of our joint work with Lingrui Ge, Jiangong You, and Qi Zhou on a non-commutative generalization of Jensen’s formula, and explain how it uncovers the mystery behind Avila’s global theory. Then, we will discuss the work of Ge and our joint work with Ge and with Ge and You, showing how the duality approach helps prove previously model-specific sharp spectral statements in a robust way. The talk is intended for a broad mathematical audience, with emphasis on ideas and mechanisms rather than technical details.
Bio-Sketch:
Svetlana Jitomirskaya is a Goldman Distinguished Chair Professor at UC Berkeley. Svetlana's research in mathematical physics has been recognized by various prizes, including the AMS Satter Prize (2005), APS & AIP Heineman Prize (2019), the inaugural Ladyzhenskaya Prize (2022), and the inaugural Barry Prize (2023). She was an invited session (2002) and plenary (2022) speaker at the ICM. She is an elected member of the AAAS, NAS, and AASL.
