Papers
- (With S. Cecchini, J. Wang and B. Zhu) Scalar curvature rigidity of the four-dimensional sphere
- (With J. Wang, G. Yu and B. Zhu) Filling Radius, Quantitative K-theory and Positive Scalar Curvature
- (With G. Tian and G. Yu) On the relative Novikov conjecture for coarsely embeddable groups
- (With S. Gong, J. Wu and G. Yu) The Novikov conjecture, the group of diffeomorphisms and continuous fields of Hilbert-Hadamard spaces
- (With J. Wang) Scalar curvature rigidity of degenerate warped product spaces
- (With J. Wang, B. Zhu and X. Zhu) Positive scalar curvature meets Ricci limit spaces
- (With J. Wang) Dihedral rigidity for submanifolds of warped product manifolds
- (With J. Wang) On Gromov's flat corner domination conjecture and Stoker's conjecture
- (With S. Weinberger and G. Yu) On Gromov's compactness question regarding positive scalar curvature
- (With J. Wang and G. Yu) On Gromov's dihedral extremality and rigidity conjectures
- (With J. Deng, G. Tian and G. Yu) K-theory of relative group C*-algebras and the relative Novikov conjecture, to appear in Mathematische Zeitschrift
- (With J. Wang and G. Yu) A proof of Gromov's cube inequality on scalar curvature, to appear in Journal of Differential Geometry
- (With J. Wang and G. Yu) Decay of scalar curvature on uniformly contractible manifolds with finite asymptotic dimension, Comm. Pure Appl. Math. 77
(2024), no. 1, 372–440.
- (with X. Chen, J. Wang and G. Yu) Delocalized eta invariants, cyclic cohomology and higher rho invariants, Ann. K-Theory 8 (2023), no. 4, 531–608.
- (with J. Wang and G. Yu) ℓ1 higher index, ℓ1 higher rho invariant and cyclic cohomology, Cyclic Cohomology at 40: Achievements and Future Prospects, Proc. Sympos. Pure Math., Vol. 105, 535–579, 2023
- A quantitative relative index theorem and Gromov's conjectures on positive scalar curvature, Journal of Noncommutative Geometry 17 (2023), no. 2, 609–662.
- (With H. Guo and G. Yu) Quantitative K-theory, positive scalar curvature, and band width, Perspectives on Scalar Curvature (edited by Gromov and Lawson) Vol. 2, 763–798, World Sci. Publ., 2023
- (With J. Wang and G. Yu) Approximations of delocalized eta invariants by their finite analogues, L'Enseignement mathématique, 69 (2023), no. 1-2, 51–91.
- (with H. Guo and G. Yu) A Lichnerowicz vanishing theorem for the maximal Roe algebra, Math. Ann. 385 (2023), no. 1-2, 717–743.
- (with G. Yu and R. Zeidler) On the range of the relative higher index and the higher rho-invariant for positive scalar curvature, Adv. Math. 390 (2021), Paper No. 107897, 24 pp
- (With H. Guo and G. Yu) Functoriality for higher rho invariants of elliptic operators, J. Funct. Anal. 280 (2021), no. 10, Paper No. 108966, 36 pp
- (with G. Yu) Delocalized eta invariants, algebraicity, and K-theory of group C*-algebras, Int. Math. Res. Not. IMRN, (2021), no. 15, 11731–11766.
- (with S. Weinberger and G. Yu) Additivity of higher rho invariants and nonrigidity of topological manifolds, Comm. Pure Appl. Math. 74 (2021), no. 1, 3–113.
- (with G. Yu) Higher Invariants in Noncommutative Geometry - On the Occasion of Alain Connes' 70th Birthday, Advances in Noncommutative Geometry, Springer, 2019
- (with A. Gorokhovsky) Fibrations and higher products in cohomology, Journal of Topology and Analysis, 11 (2019), no. 1, 135–147.
- (with A. Gorokhovsky and D. Sullivan)
Generalized Euler classes, differential forms and commutative DGAs, Journal of Topology and Analysis, 11 (2019), no. 1, 109–118.
- (with N. Higson ) Higher signatures on Witt spaces
- (with N. Higson and T. Schick) On C*-Algebraic Higher Signatures and an Invariance Theorem in Codimension Two, Geom. Topol. 22 (2018) no.6, 3671–3699
- (with G. Yu) Higher rho invariants and the moduli space of positive scalar curvature metrics, Advances in Mathematics 307 (2016), 1046–1069
- (with G. Yu) Noncommutative Geometry of Discrete Groups, Introduction to modern mathematics, 425 - 432, Adv. Lect. Math. (ALM) 33, 2015.
- (with G. Yu) Positive
scalar curvature, higher rho invariants and localization
algebras, Advances in Mathematics 262 (2014), 823–866.
- (with G. Yu) A relative higher index theorem, diffeomorphisms and positive scalar curvature,
Advances in Mathematics, 250 (2014), 35–73.
- The odd
dimensional analogue of a theorem of Getzler and Wu,
Journal of Noncommutative Geometry, 7 (2013), no. 3, 647–676.
- Relative index
pairing and odd index theorem for even dimensional manifolds,
Journal of Functional Analysis, 260 (2011), no. 7, 2064–2085
Preprints
- (with J. Deng and G. Yu) Novikov conjecture for groups generated by coarsely embeddable groups under extensions and direct limits