Boyu Zhang

Department of Mathematics, Princeton University
Fine Hall, Princeton, NJ 08540
Office: Fine Hall 602
email: bz at math dot princeton dot edu




I am a math instructor at Princeton University. I completed my Ph.D. at Harvard University in 2018 advised by Clifford Taubes. My research interest is in gauge theory, symplectic geometry, and low dimensional topology. In particular, I am interested in applications of gauge theory to the study of geometric structures on three and four-dimensional manifolds, such as foliations, contact structures, and symplectic structures. Here is my CV.



Research

  1. Instantons and Khovanov skein homology on I×T2 (Joint with Yi Xie)
    arXiv:2005.12863

  2. Two detection results of Khovanov homology on links (Joint with Zhenkun Li and Yi Xie)
    arXiv:2005.05897

  3. On links with Khovanov homology of small ranks (Joint with Yi Xie)
    arXiv:2005.04782

  4. Classification of links with Khovanov homology of minimal rank (Joint with Yi Xie)
    arXiv:1909.10032

  5. Instanton Floer homology for sutured manifolds with tangles (Joint with Yi Xie)
    arXiv:1907.00547

  6. On the compactness problem for a family of generalized Seiberg-Witten equations in dimension three (Joint with Thomas Walpuski)
    arXiv:1904.03749

  7. Rectifiability and Minkowski bounds for the zero loci of Z/2 harmonic spinors in dimension 4
    arXiv:1712.06254

  8. Modulo 2 counting of Klein-bottle leaves in smooth taut foliations
    Algebraic & Geometric Topology 18 (2018) 2701-2727

  9. A monopole Floer invariant for foliations without transverse invariant measure
    arXiv:1603.08136



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

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)