Guo Hao

Assistant Professor

Yau Mathematical Science Center, Tsinghua University

Office: Ning Zhai W07


Personal web page

Research Areas

Index theory, noncommutative geometry, operator algebras.

Educational Background

2016-2018 PhD, University of Adelaide

Work Experience

2022-present Assistant Professor, Yau Mathematical Science Center, Tsinghua University

2018-2021 Visiting Assistant Professor, Texas A&M University

Honors and Awards

2019 Outstanding Teaching Award, Texas A&M Department of Mathematics

2018 Dean's Commendation for Doctoral Thesis Excellence, University of Adelaide

2016 B.H. Neumann Prize, Australian Mathematical Society       



·A geometric Elliott invariant and noncommutative rigidity of mapping tori (with V. Proietti and H. Wang).


·Covering complexity, scalar curvature, and quantitative K-theory (with G. Yu)


·Higher localised A-hat-genera for proper actions and applications (with V. Mathai).


·Quantitative K-theory, positive scalar curvature, and band width (with Z. Xie and G. Yu).

Perspectives on Scalar Curvature, eds. M. Gromov and H. B. Lawson (Accepted)

·An Equivariant Poincare duality for proper cocompact actions by matrix groups (with V. Mathai).

Journal of Noncommutative Geometry (Accepted)

·A Lichnerowicz vanishing theorem for the maximal Roe algebra (with Z. Xie and G. Yu).

Mathematische Annalen (2021)

·Functoriality for higher rho Invariants of elliptic operators (with Z. Xie and G. Yu).

Journal of Functional Analysis (2021)

·Coarse geometry and Callias quantisation (with P. Hochs and V. Mathai).

Transactions of the American Mathematical Society (2020)

·Equivariant Callias index theory via coarse geometry (with P. Hochs and V. Mathai).

Annales de l’Institut Fourier (2020)

·Positive scalar curvature and an equivariant Callias-type index theorem for proper actions (with P. Hochs and V. Mathai).Annals of K-theory (2020)

·Index of G-Callias-type operators and G-invariant metrics of positive scalar curvature.

Journal of Geometric Analysis (2019)

·Positive scalar curvature and Poincare duality for proper actions (with V. Mathai and H. Wang).

Journal of Noncommutative Geometry (2019)

·Positive scalar curvature and Callias-type index theorems for proper actions.

Bulletin of the Australian Mathematical Society (2019)

·A Poincaré duality in K-theory. Australian Mathematical Society Gazette (2017)