The Dry Ten Martini Problem for Sturmian Schrodinger Operators

Explore the intricacies of the dry ten Martini problem for Sturmian Schrodinger operators in this seminar talk from the Spectral Geometry in the clouds series. Delve into the history of the Ten Martini Problem and its dry counterpart, originally posed for the Almost-Mathieu operator. Examine the connection between spectral gaps and the integrated density of states in one-dimensional Schrödinger operators with aperiodic Sturmian sequence potentials. Learn about recent breakthroughs in solving the Dry Ten Martini Problem for Sturmian Schrödinger operators, including the speaker's joint work that provides a solution for all irrational frequencies and coupling constants. Gain insights into the mathematical challenges and techniques involved in addressing this long-standing problem in spectral theory.