6 papers
Discrete Mixed Quantization for Cat Maps
Elena Kim, Qiaochu Ma
In this paper, we develop a mixed quantization technique for graph vector bundles that combines semiclassical analysis and quantum cat maps. We apply it to study the Kesten--McKay…
Gromov's Simplicial Volume Vanishing Conjecture for Positive Scalar Curvature
Qiaochu Ma, Jinmin Wang, Zhizhang Xie +2
In this paper, we prove Gromov's simplicial volume vanishing conjecture for closed manifolds with spin universal cover. More precisely, we show that if a closed oriented manifold a…
Discrete Mixed Quantization
Qiaochu Ma
In this paper, we develop a mixed quantization technique for graph vector bundles and apply it to several asymptotic spectral problems, including the Alon-Boppana bound, the Kesten…
Small scale index theory, scalar curvature, and Gromov's simplicial norms
Qiaochu Ma, Guoliang Yu
In this article, we study the topological complexity of manifolds with a lower scalar curvature bound. We introduce a small scale index theorem to establish an upper bound for Grom…
Superconnections and Bott-Chern valued Riemann-Roch-Grothendieck for complex orbifolds, I
Qiaochu Ma, Xiang Tang, Hsian-Hua Tseng +1
We use flat antiholomorphic superconnections to study orbifold Chern character following the method introduced by Bismut, Shen, and Wei on general complex orbifolds. We show the un…
Bounding the A-hat genus using scalar curvature lower bounds and isoperimetric constants
Qiaochu Ma, Jinmin Wang, Guoliang Yu +1
In this paper, we prove an upper bound on the genus of a smooth, closed, spin Riemannian manifold using its scalar curvature lower bound, Neumann isoperimetric consta…