Speaker: Prof. Linfeng Li (Southern University of Science and Technology)

Title: Nodal sets and observability via quantitative unique continuation

Time: 10:00–11:00, October 23, 2026 (Friday)

Inviter: Prof. Jinping Zhuge (MCM, CAS)

Venue: MCM110

Abstract: Quantitative unique continuation is a fundamental property of partial differential equations, which asserts that the smallness of a solution at one scale quantitatively controls its behavior at larger scales. It plays an important role in the study of nodal sets and in problems from control theory. While Yau's conjecture on nodal set remains open in full generality, there has been significant progress in recent years. In this talk, I will present a new result on the nodal sets of parabolic equations, which extend Yau's conjecture to solutions with Gevrey regularity. Subsequently, I will explore applications of quantitative unique continuation to observability inequalities in control theory, which asserts that global behavior can be determined from partial information.