The UAB Department of Mathematics will host the 2025 Roger T. Lewis Endowed Lectureship in Mathematics. 

This year, the lecture will feature Svetlana Jitomirskaya, Ph.D., professor in the Department of Mathematics at UC Berkeley. Her talk is titled, "Dual Lyapunov Exponents and the Robust Ten Martini Problem."

The Hofstadter butterfly, a plot of the band spectra of almost Mathieu operators at rational frequencies, has become a pictorial symbol of the field of quasiperiodic operators. It is visually clear from this plot that for all irrational frequencies the spectrum must be a Cantor set, a statement that has been dubbed the ten martini problem, a name coined by Barry Simon. It has been established for the almost Mathieu operators, exploiting various special features of this family. We will discuss a recently developed robust method allowing to establish it for a large class of one-frequency quasiperiodic operators, including nonperturbative analytic neighborhoods of several popular explicit families. The proof builds on the recently developed concept of dual Lyapunov exponents and partial hyperbolicity of the dual cocycles. 

A reception will take place at 3:00 p.m. in the University Hall lobby, and the lecture will take place at 3:30 p.m. in UHALL 1005.