At the 1981 AMS Annual Meeting, Mark Kac famously asked whether the almost Mathieu operator “has all its gaps there.” He jokingly offered ten martinis to whoever could solve it. Later, Barry Simon split Kac’s question into two parts: the simpler one, known as the Ten Martini Problem, and the harder one, the Dry Ten Martini Problem. Forty-four years later, the original dry version remains open. Nevertheless, some progress has been made. In this talk, we will show that the Dry Ten Martini Problem holds for a class of non–almost Mathieu operators with all irrational frequencies. The proof is based on analyzing the projective action of Hermitian symplectic cocycles, a fundamental structure underlying quasiperiodic Schrödinger operators. This is joint work with D. Xu and Q. Zhou.