Photo of me Joshua X. Wang

Office: Science Center 425a


Curriculum Vitae

I'm a fifth-year graduate student in mathematics at Harvard, and my Ph.D. advisor is Peter Kronheimer. Next year, I'll be at MIT as an NSF Postdoctoral Fellow. After that, I'll be at Princeton and the IAS as a Veblen Research Instructor.

My main areas of research are low-dimensional topology, Floer theory, and categorification.

Peter Kronheimer, Fan Ye, and I are organizing the Gauge Theory and Topology Seminar this semester.


  1. The Gysin sequence and the sl(N) homology of T(2,m)

    preprint | arXiv

  2. Colored sl(N) homology and SU(N) representations of the trefoil

    preprint | arXiv

  3. Split link detection for sl(P) link homology in characteristic P

    Journal of Topology, under revision | arXiv

  4. On sl(N) link homology with mod N coefficients

    Quantum Topology, accepted | arXiv

  5. Link Floer homology also detects split links

    Bulletin of the London Mathematical Society 53 (4): 1037-1044 (2021) | arXiv

  6. The cosmetic crossing conjecture for split links

    Geometry & Topology 26 (7): 2941-3053 (2022) | arXiv

  7. A combinatorial proof of invariance of double-point enhanced grid homology
    with Timothy Ratigan and Luya Wang

    preprint | arXiv


Minor thesis - Hodge theory for matroids

Teaching and Mentoring

Fall 2021 - Math 21a: Multivariable calculus


Spring 2021 - Low-dimensional manifolds

Summer 2020 - Differential forms in algebraic topology

Summer 2019 - Knot invariants and category theory with Morgan Opie

Directed Reading Program

I used to organize the Directed Reading Program, and I've mentored five reading projects.


Some photos of knots and links made from pretzels, baked at a birthday get-together.