Department of Mathematics, University of Maryland at College Park
Office: 4418 Kirwan Hall
Email: bzh at umd.edu
I am teaching MATH 734: Algebraic Topology in Spring 2024. Course information can be found here.
I am an assistant professor at the University of Maryland at College Park.
Before joining the University of Maryland, I was an instructor of mathematics at Princeton University from 2018 to 2021, and an assistant professor of mathematics at Princeton University from 2021 to 2022. I completed my Ph.D. at Harvard University in 2018 advised by Clifford Taubes. Here is my CV.
My research interest is in gauge theory, Floer homology, and their interactions with geometric structures on 3 and 4-dimensional manifolds such as knots and links, foliations, contact structures, and symplectic structures.
Ring structures in singular instanton homology
(Joint with Yi Xie) arXiv
A deformation of Asaeda-Przytycki-Sikora homology
(Joint with Zhenkun Li and Yi Xie)
accepted by Algebr. Geom. Topol. arXiv
Instanton homology and knot detection on thickened surfaces
(Joint with Zhenkun Li and Yi Xie)
Selecta Math. 29, Article number: 84 (2023)
journal,
arXiv
A note on the existence of U-cyclic elements in periodic Floer homology
(Joint with Dan Cristofaro-Gardiner, Daniel Pomerleano, and Rohil Prasad),
accepted by Proc. Amer. Math. Soc.
arXiv
The smooth closing lemma for area-preserving surface diffeomorphisms
(Joint with Dan Cristofaro-Gardiner and Rohil Prasad)
arXiv
On Floer minimal knots in sutured manifolds (Joint with Zhenkun Li and Yi Xie)
Trans. Amer. Math. Soc. Ser. B 9 (2022), 499-516 journal, arXiv
On meridian-traceless SU(2)-representations of link groups (Joint with Yi Xie)
Adv. Math. Volume 418 (2023), 108947 journal, arXiv
Equivariant Cerf theory and perturbative SU(n) Casson invariants (Joint with Shaoyun Bai) arXiv
Instantons and Khovanov skein homology on I×T^{2} (Joint with Yi Xie)
accepted by Quantum Topol. arXiv
Two detection results of Khovanov homology on links (Joint with Zhenkun Li and Yi Xie)
Trans. Amer. Math. Soc. 374 (2021), 6649-6664
journal,
arXiv
On links with Khovanov homology of small ranks (Joint with Yi Xie)
Math. Res. Lett. Volume 29 (2022), Number 4, 1261-1277
journal,
arXiv
Classification of links with Khovanov homology of minimal rank (Joint with Yi Xie)
J. Eur. Math. Soc. (2023), journal, arXiv
Instanton Floer homology for sutured manifolds with tangles (Joint with Yi Xie)
accepted by J. Differential Geom.
arXiv
On the compactness problem for a family of generalized Seiberg-Witten equations in dimension three (Joint with Thomas Walpuski)
Duke Math. J. 170(17):3891-3934 (2021)
journal,
arXiv
Rectifiability and Minkowski bounds for the zero loci of Z/2 harmonic spinors in dimension 4
Commun. Anal. Geom., Volume 30 (2022), Number 7, Pages: 1633 - 1681
journal,
arXiv
Modulo 2 counting of Klein-bottle leaves in smooth taut foliations
Algebr. Geom. Topol. 18 (2018) 2701-2727 journal,
arXiv
Monopoles and foliations without holonomy-invariant transverse measure
J. Symplectic Geom. Volume 20 (2022), Number 1, 191 - 258
journal, arXiv
Yue Wang, Boyu Zhang, Jeremie Kropp, Nadya Morozova:
Inference on tissue transplantation experiments
Journal of Theoretical Biology, Volume 520 (2021).
Hui Zhao, Kehua Su, Chenchen Li, Boyu Zhang, Lei Yang, Na Lei, Xiaoling Wang, Steven J. Gortler, Xianfeng Gu:
Mesh Parametrization Driven by Unit Normal Flow
Computer Graphics Forum, Volume 39, Issue 1 (2019).
A note on the hypoellipticity of Folland-Stein heat operators
On Mostow's Rigidity Theorem (Minor thesis supervised by Curtis T. McMullen)