Qiaochu Ma 马翘楚
Qiaochu Ma 马翘楚
Texas A&M University
155 Ireland Street, College Station, Texas 77840
Email: qiaochu"at"tamu.edu
Texas A&M University
155 Ireland Street, College Station, Texas 77840
Email: qiaochu"at"tamu.edu
Research Fields:
I was trained as a geometer, working primarily on Atiyah-Singer index theory and its interactions with complex geometry, scalar curvature geometry, and noncommutative geometry.
Motivated by questions on asymptotic spectral invariants in index theory, I have also developed, together with collaborators, an analytic technique called mixed quantization. This technique brings together semiclassical quantization and geometric quantization, and has led us to study quantum chaos, harmonic analysis, partially hyperbolic dynamics, and discrete probability, areas that, at first sight, seem quite far from index theory.
Positions:
I completed my Ph.D. at Université Paris Cité, France, under the supervision of Prof. Xiaonan Ma. From August 2022 to July 2024, I was a postdoctoral researcher at Penn State University under the direction of Prof. Nigel Higson. In August 2024, I joined Texas A&M University as a Visiting Assistant Professor, working with Prof. Sherry Gong and Prof. Guoliang Yu.
Publications and Preprints:
Local Atiyah-Singer Index Theory
Small scale index theory, scalar curvature, and Gromov's simplicial norms, with Guoliang Yu, arXiv:2508.14791, 2025, 46 pages.
Superconnection and orbifold Chern character, with Xiang Tang, Hsian-Hua Tseng, Zhaoting Wei, arXiv: 2505.13912, 2025, 55 pages.
Bounding the A-hat genus using scalar curvature lower bounds and isoperimetric constants, with Jinmin Wang, Guoliang Yu, Bo Zhu, J. Geom. Anal. 201 (36) (2026), 10 pages, PDF COPY.
Toeplitz operators and the full asymptotic torsion forms, J. Funct. Anal. 286 (3) (2024), Paper No.110210, 74 pages, PDF COPY.
Mixed Quantization
Discrete Mixed Quantization, arXiv: 2605.16203, 2026, 80 pages.
Arithmetic unique ergodicity for infinite dimensional flat bundles, arXiv: 2411.12302, 2024, 17 pages.
Mixed quantization and partial hyperbolicity, with Snir Ben Ovadia and Federico Rodriguez-Hertz, arXiv:2409.13660, 2024, 20 pages.
Semiclassical analysis, geometric representation and quantum ergodicity, with Minghui Ma, Commun. Math. Phys. 405, 259 (2024), 28 pages, PDF COPY.