Boyu Zhang

Research

1. Ring structures in singular instanton homology
   (Joint with Yi Xie) arXiv

2. A deformation of Asaeda-Przytycki-Sikora homology
   (Joint with Zhenkun Li and Yi Xie) arXiv

3. Instanton homology and knot detection on thickened surfaces
   (Joint with Zhenkun Li and Yi Xie)
   Selecta Math. 29, Article number: 84 (2023) journal, arXiv

4. 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

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

6. 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

7. On meridian-traceless SU(2)-representations of link groups (Joint with Yi Xie)
   Adv. Math. Volume 418 (2023), 108947 journal, arXiv

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

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

10. 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

11. On links with Khovanov homology of small ranks (Joint with Yi Xie)
    Math. Res. Lett. Volume 29 (2022), Number 4, 1261-1277 journal, arXiv

12. Classification of links with Khovanov homology of minimal rank (Joint with Yi Xie)
    J. Eur. Math. Soc. (2023), journal, arXiv

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

14. 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

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

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

17. Monopoles and foliations without holonomy-invariant transverse measure
    J. Symplectic Geom. Volume 20 (2022), Number 1, 191 - 258 journal, 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

Past Teaching Experiences