Photo of me Joshua X. Wang

Office: 2-252B


Curriculum Vitae

I'm an NSF Postdoctoral Fellow in the Department of Mathematics at MIT, and Tom Mrowka is my faculty mentor. I was a graduate student in mathematics at Harvard, advised by Peter Kronheimer.

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

MIT Geometry and Topology Seminar


  1. A minimality property for knots without Khovanov 2-torsion

    with Onkar Singh Gujral

    preprint | arXiv

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

    Proceedings for "Frontiers in Geometry and Topology", accepted | arXiv

  3. Colored sl(N) homology and SU(N) representations I: the trefoil and the Hopf link

    preprint | arXiv

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

    Journal of Topology 16 (2): 806-821 (2023) | arXiv

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

    Quantum Topology, accepted | arXiv

  6. Link Floer homology also detects split links

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

  7. The cosmetic crossing conjecture for split links

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

  8. A combinatorial proof of invariance of double-point enhanced grid homology

    with Timothy Ratigan and Luya Wang

    preprint | arXiv


Minor thesis (Ph.D. requirement) - Hodge theory for matroids

Teaching and Mentoring

The Graduate School of Arts and Sciences at Harvard presented me with the Derek C. Bok Award!

Courses at Harvard

Fall 2021 - Math 21a: Multivariable calculus

Spring 2021 - Tutorial: Low-dimensional manifolds

Summer 2020 - Tutorial: Differential forms in algebraic topology

Summer 2019 - Tutorial: Knot invariants and category theory with Morgan Opie

I helped start and organize the Directed Reading Program at Harvard while I was a graduate student.


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