报告人：龚禹霖（清华大学)

时间：7月5日，16:30-17:30

地点：2205

题目: The spectral concentration and sublinear lower bound for twisted Laplacian on compact hyperbolic surfaces

摘要: In this talk, we investigate the asymptotic spectral distribution of the twisted Laplacian associated with a real harmonic 1-form on a compact hyperbolic surface. Our main results concern both upper and lower bounds for the eigenvalue counting function. First, we show that most eigenvalues lie in certain regions where the imaginary parts converge logarithmically to their average as the real parts tend to infinity. The proof relies on moderate deviation principles for Anosov geodesic flows. Second, we establish a sublinear lower bound on the number of eigenvalues contained in a sufficiently large strip, determined by dynamical quantities associated with the harmonic 1-form. This is joint work with Long Jin.