Photo of me Joshua Wang

Princeton University

Office: Fine Hall 407
Email: joshuaxw@princeton.edu


Institute for Advanced Studies

Office: MOS 112
Email: jxwang@ias.edu


Curriculum Vitae

I'm a Veblen Research Instructor at Princeton and the IAS. I'm also an NSF Postdoctoral Fellow, and I'm affliated with a Simons Collaboration. Previously, I was an NSF and Simons postdoc at MIT after completing my PhD in mathematics at Harvard, advised by Peter Kronheimer. I was an undergraduate at Princeton before that, and I'm very happy to be back!

My main areas of research are in low-dimensional topology: Floer theory and categorification. My training was in applications of gauge theory to low-dimensional topology, while my more recent interests touch representation theory, algebraic combinatorics, and other parts of geometry and topology.



Research

  1. Stable deformed gl(N) homology of torus knots

    with William Ballinger, Eugene Gorsky, and Matthew Hogancamp

    preprint | arXiv

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

    with Onkar Singh Gujral

    Algebraic and Geometric Topology, accepted | arXiv

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

    Proceedings of Symposia in Pure Mathematics 109: 233-251 (2024) | arXiv

  4. Colored sl(N) homology and SU(N) representations

    Advances in Mathematics 474 (2025) 110314 | arXiv

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

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

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

    Quantum Topology 15 (1): 87-121 (2024) | arXiv

  7. Link Floer homology also detects split links

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

  8. The cosmetic crossing conjecture for split links

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

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

    with Timothy Ratigan and Luya Wang

    Journal of Knot Theory and Its Ramifications, accepted | arXiv



Teaching and Mentoring

Courses at Princeton

Spring 2025 - MAT 218: Multivariable Analysis and Linear Algebra II

Fall 2024 - MAT 216: Multivariable Analysis and Linear Algebra I


Courses at MIT

Spring 2024 - 18.099: Independent Study in Mathematics (Low-dimensional topology)

Fall 2023 - 18.099: Independent Study in Mathematics (The geometry of complex analysis)


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


Directed Reading Programs (DRP)

I co-organized the MIT DRP during 2023-2024, and I mentored two reading projects.

I started and co-organized the Harvard DRP during 2018-2023, and I mentored five reading projects.


Research mentoring

I'm mentoring a high school research project through MIT PRIMES during 2024.



Exposition

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



Personal

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