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 (my PSU email has been deactivated, please do NOT send emails to it)
Texas A&M University
155 Ireland Street, College Station, Texas 77840
Email: qiaochu"at"tamu.edu (my PSU email has been deactivated, please do NOT send emails to it)
Research Fields:
I was trained as a geometer, working primarily on the Atiyah-Singer index theory and its interfaces with complex geometry, scalar curvature geometry, and noncommutative geometry.
Also, motivated by questions about asymptotic spectral invariants in index theory, I developed, together with collaborators, an analytic technique called mixed quantization and used it to study quantum chaos and partially hyperbolic dynamics, areas that are, at first sight, quite far from index theory.
Positions:
I completed my Ph.D. study 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, 46pp.
Superconnection and orbifold Chern character, with Xiang Tang, Hsian-Hua Tseng, Zhaoting Wei, arXiv: 2505.13912, 2025, 55pp.
Bounding the A-hat genus using scalar curvature lower bounds and isoperimetric constants, with Jinmin Wang, Guoliang Yu, Bo Zhu, arXiv:2410.08866, 2025, 10pp.
Toeplitz operators and the full asymptotic torsion forms, J. Funct. Anal. 286 (3) (2024), Paper No.110210, 74pp, PDF COPY.
Quantum Chaos
Arithmetic unique ergodicity for infinite dimensional flat bundles, arXiv: 2411.12302, 2024, 17pp.
Mixed quantization and partial hyperbolicity, with Snir Ben Ovadia and Federico Rodriguez-Hertz, arXiv:2409.13660, 2024, 20pp.
Semiclassical analysis, geometric representation and quantum ergodicity, with Minghui Ma, Commun. Math. Phys. 405, 259 (2024), 28pp, PDF COPY.