Oberseminar "Geometrische Analysis und Zahlentheorie": Zhongkai Tao (UC Berkeley) (online)

We prove the strong convergence of the spectrum of the kinetic Brownian motion to the spectrum of base Laplacian for locally symmetric spaces. This generalizes recent work of Kolb--Weich--Wolf on constant curvature surfaces in two aspects. First we give a construction of Casimir operators for a large family of locally homogeneous spaces, including all locally symmetric spaces. Second, we analyze the spectrum carefully using the Schur complement formula and prove a strong convergence by studying projections to the spherical harmonics. This is joint work with Qiuyu Ren.