8 papers
Eigenvalue rigidity of hyperbolic surfaces in the random cover model
Elena Kim, Zhongkai Tao
Let be a compact connected orientable hyperbolic surface and let be a degree random cover. We show that, with high probability, the distribution of eigenvalues of the…
Generic twisted Pollicott--Ruelle resonances and zeta function at zero
Tristan Humbert, Zhongkai Tao
For a connected orientable closed surface of genus with Anosov geodesic flow, we show the existence of an open subset of finite-dimensional irreducible represent…
Spectral gap for surfaces of infinite volume with negative curvature
Zhongkai Tao
We prove that the imaginary parts of scattering resonances for negatively curved asymptotically hyperbolic surfaces are uniformly bounded away from zero and provide a resolvent bou…
Lossless Strichartz and spectral projection estimates on unbounded manifolds
Xiaoqi Huang, Christopher D. Sogge, Zhongkai Tao +1
We prove new lossless Strichartz and spectral projection estimates on asymptotically hyperbolic surfaces, and, in particular, on all convex cocompact hyperbolic surfaces. In order…
Integral formulas for under/overdetermined differential operators via recovery on curves and the finite-dimensional cokernel condition I: General theory
Philip Isett, Yuchen Mao, Sung-Jin Oh +1
We introduce a new versatile method for constructing solution operators (i.e., right-inverses up to a finite rank operator) for a wide class of underdetermined PDEs , whic…
Fragile topology on solid grounds: a mathematical perspective
Simon Becker, Zhongkai Tao, Mengxuan Yang
This paper provides a mathematical perspective on fragile topology phenomena in condensed matter physics. In dimension , vanishing Chern classes of bundles of Bloch eigen…