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. 2) On splitting rank of non-compact type symmetric spaces and bounded cohomology. J. Topol. Anal. 12 (2020), pgs. 465-489. 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. 4) Some remarks on the simplicial volume of nonpositively curved manifolds (with Chris Connell). Math. Ann. 377 (2020), pgs. 969-987. 5) Homological norms on nonpositively curved manifolds (with Chris Connell). Comment. Math. Helv. 97 (2022), pgs. 801–825. 6) Cheeger-Gromoll splitting theorem for groups (with Thang Nguyen). Algebr. Geom. Topol. 22 (2022), pgs. 3377-3399. 7) Discrete subgroups of small critical exponent (with Beibei Liu). Geom. Topol. 27 (2023), pgs.2347-2381. 8) Geometric cycles and bounded cohomology for a cocompact lattice in SLn(R). Math. Z. 301 (2022), pgs. 3109-3125. 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). 10) Cusps, Kleinian groups and Eisenstein series (with Beibei Liu). Forum Math. Sigma. (2023) Vol. 11:e75 1-22. 11) An L1-norm-mass inequality for complete manifolds (with Caterina Campagnolo). Ann. Inst. Fourier (Grenoble). (2024) no. 3, pgs. 1297-1318. 12) Marked length spectrum rigidity for relatively hyperbolic groups (with Thang Nguyen). Kyoto J. Math.(2024) to appear. 13) The natural flow and the critical exponent (with Chris Connell and D. B. McReynolds). Submitted. https://arxiv.org/abs/2302.12665 14) Nonpositively curved 4-manifolds with zero Euler characteristic (with Chris Connell and Yuping Ruan). Submitted. https://arxiv.org/abs/2309.15766 15) Simplicial volume and isolated, closed totally geodesic submanifolds of codimension one (with Chris Connell and Yuping Ruan). Submitted. https://arxiv.org/abs/2410.19981 16) Average signature of geodesic paths in compact Lie groups (with Chong Liu). Submitted. https://arxiv.org/abs/2411.06760 17) Homological dimension of discrete subgroups in higher rank Lie groups (with Chris Connell and D. B. McReynolds). https://arxiv.org/abs/2504.18923 |
Email:wangshi@shanghaitech.edu.cn Office: S421, School of Creativity & Arts |
