Boyu Zhang

Department of Mathematics, University of Maryland at College Park
Office: 4118 Kirwan Hall
Email: bzh at umd.edu




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.



Research

  1. Instanton homology and knot detection on thickened surfaces
    (Joint with Zhenkun Li and Yi Xie) arXiv

  2. 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

  3. The smooth closing lemma for area-preserving surface diffeomorphisms
    (Joint with Dan Cristofaro-Gardiner and Rohil Prasad) arXiv

  4. On Floer minimal knots in sutured manifolds (Joint with Zhenkun Li and Yi Xie)
    Trans. Amer. Math. Soc. Ser. B 9 (2022), 499-516 published version, arXiv

  5. On meridian-traceless SU(2)-representations of link groups (Joint with Yi Xie) arXiv

  6. Equivariant Cerf theory and perturbative SU(n) Casson invariants (Joint with Shaoyun Bai) arXiv

  7. Instantons and Khovanov skein homology on I×T2 (Joint with Yi Xie)
    accepted by Quantum Topol. arXiv

  8. Two detection results of Khovanov homology on links (Joint with Zhenkun Li and Yi Xie)
    Trans. Amer. Math. Soc. 374 (2021), 6649-6664 published version, arXiv

  9. On links with Khovanov homology of small ranks (Joint with Yi Xie)
    accepted by Math. Res. Lett. arXiv

  10. Classification of links with Khovanov homology of minimal rank (Joint with Yi Xie)
    accepted by J. Eur. Math. Soc. arXiv

  11. Instanton Floer homology for sutured manifolds with tangles (Joint with Yi Xie) arXiv

  12. 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) published version, arXiv

  13. Rectifiability and Minkowski bounds for the zero loci of Z/2 harmonic spinors in dimension 4
    accepted by Commun. Anal. Geom. arXiv

  14. Modulo 2 counting of Klein-bottle leaves in smooth taut foliations
    Algebr. Geom. Topol. 18 (2018) 2701-2727 published version, arXiv

  15. Monopoles and foliations without holonomy-invariant transverse measure
    accepted by J. Symplectic Geom. arXiv



Interdisciplinary collaborations

  1. Yue Wang, Boyu Zhang, Jeremie Kropp, Nadya Morozova: Inference on tissue transplantation experiments
    Journal of Theoretical Biology, Volume 520 (2021).

  2. 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).



Expository writings

A note on the hypoellipticity of Folland-Stein heat operators

On Mostow's Rigidity Theorem (Minor thesis supervised by Curtis T. McMullen)



Teaching at UMD

MATH 432: Introduction to Topology (Fall 2022)


Past Teaching Experiences

MAT 204: Advanced Linear Algebra with Applications (Princeton, Spring 2022)
MAT 215: Single Variable Analysis with an Introduction to Proofs (Princeton, Fall 2021)
MSRI Summer School 2021: An introduction to Yang-Mills equations
MAT 175: Mathematics for Economics and Life Sciences (Princeton, Fall 2020, Spring 2021)
Undergraduate Reading course: Topics in Gauge Theory (Princeton, Spring 2021)
MAT 567: Topics in Low Dimensional Topology: Yang-Mills Equation and Instanton Floer Homology (Princeton, Spring 2020)
Undergraduate Reading course: Morse Theory (Princeton, Fall 2019)
MAT 175: Mathematics for Economics and Life Sciences (Princeton, Fall 2019)
Math 104: Calculus II (Princeton, Fall 2018, Spring 2019)
Math 1b: Calculus, Series, and Differential Equations. (Harvard, Spring 2017)
Undergraduate Tutorial: Morse Theory (Harvard, Spring 2016)
Summer Tutorial: Knots and Links (Harvard, Summer 2015)
Qualifying Exam Tutorial (Harvard, Summer 2015)
Math 1b: Calculus, Series, and Differential Equations. (Harvard, Spring 2015)
Qualifying Exam Tutorial (Harvard, Summer 2014)