Career • 2022.7--present, Assistant Professor, ShanghaiTech University • 2021.1--2022.7, Postdoc, Michigan State University • 2019.7--2020.12, Postdoc, Max Planck Institute for Mathmatics • 2016.8--2019.5, Zorn Postdoctoral Fellow, Indiana University Education • 2010.8--2016.6, Ph. D in Mathematics, The Ohio State Univesity • 2006.9--2010.6, B.S. in Mathematics, Zhejiang University Research Interest I have broad interests in the areas of differential geometry, geometric topology, geometric group theory and dynamical systems. I am particularly interested in Gromov norm (simplicial volume) and bounded cohomology of non-positively curved spaces. More recently, I study the discrete isometry subgroups (typically infinite volume) of Hadamard manifolds, especially on how the critical exponent interacts with the geometry and topology of the quotient manifold. Selected Publications 1) Barycentric straightening and bounded cohomology (with Jean-François Lafont) J. Eur. Math. Soc. 21 (2019), pgs. 381-403. Arxiv link 2) On splitting rank of non-compact type symmetric spaces and bounded cohomology. J. Topol. Anal. 12 (2020), pgs. 465-489. Arxiv link 3) Positivity of simplicial volume for nonpositively curved manifolds with a Ricci-type curvature condition (with Chris Connell). Groups Geom. Dyn.13 (2019), pgs. 1007-1034.Arxiv link 4) Some remarks on the simplicial volume of nonpositively curved manifolds (with Chris Connell). Math. Ann.377 (2020), pgs. 969-987.Arxiv link 5) Homological norms on nonpositively curved manifolds (with Chris Connell). Comment. Math. Helv. 97 (2022), pgs. 801–825.Arxiv link 6) Cheeger-Gromoll splitting theorem for groups (with Thang Nguyen). Algebr. Geom. Topol. 22 (2022), pgs. 3377-3399. Arxiv link 7) Discrete subgroups of small critical exponent (with Beibei Liu). Geom. Topol.27 (2023), pgs.2347-2381. Arxiv link 8) Geometric cycles and bounded cohomology for a cocompact lattice in SLn(R). Math. Z. 301 (2022), pgs. 3109-3125.Arxiv link 9) Positivity of simplicial volume via barycentric techniques. (in Proceedings of the International Young Seminars on Bounded Cohomology and Simplicial Volume, ed. C. Campagnolo, F. Fournier-Facio, N. Heuer and M. Moraschini). LMS Lecture Notes,(2022). Link 10) Cusps, Kleinian groups and Eisenstein series (with Beibei Liu). Forum Math. Sigma. (2023) Vol. 11:e75 1-22, Arxiv link 11) An L1-norm-mass inequality for complete manifolds (with Caterina Campagnolo). Ann. Inst. Fourier (Grenoble). (2024) no. 3, pgs. 1297-1318. Arxiv link 12) Marked length spectrum rigidity for relatively hyperbolic groups (with Thang Nguyen). Kyoto J. Math.(2024) to appear, Arxiv link 13) The natural flow and the critical exponent (with Chris Connell and D. B. McReynolds). Submitted. Arxiv link 14) Nonpositively curved 4-manifolds with zero Euler characteristic (with Chris Connell and Yuping Ruan). Adv. Math. 484 (2026), Paper No. 110680.Arxiv link 15) Simplicial volume and isolated, closed totally geodesic submanifolds of codimension one (with Chris Connell and Yuping Ruan). Submitted.Arxiv link 16) Average signature of geodesic paths in compact Lie groups (with Chong Liu). J. Lond. Math. Soc. 113 (2026) e70596, Arxiv link 17) Homological dimension of discrete subgroups in higher rank Lie groups (with Chris Connell and D. B. McReynolds). Not intend to submit yet. Arxiv link 18) On the Jacobian of the Douady-Earle extension (with Chris Connell and Yuping Ruan). Submitted. Arxiv link 19) Signature inversion of C^1-axial linear curves (with Chong Liu). Submitted. Arxiv link |
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