Photo of me Joshua X. Wang

Office: Science Center 425a


I'm a fourth-year graduate student in mathematics at Harvard, and my main area of research is low-dimensional topology. My Ph.D. advisor is Peter Kronheimer.

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

Curriculum Vitae


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

    preprint | arXiv

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

    preprint | arXiv

  3. Link Floer homology also detects split links

    Bulletin of the London Mathematical Society (2021) | arXiv

  4. The cosmetic crossing conjecture for split links

    Geometry & Topology, accepted | arXiv

  5. 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 - Teaching evaluations

Summer 2020 - Differential forms in algebraic topology - Teaching evaluations

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 so far.


My partner Teresa Tang draws dugongs and has published a sticker pack for iMessage!

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