Photo of me Joshua Wang

Princeton University

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


Institute for Advanced Study

Office: Fuld Hall 117 (previously MOS 112)
Email: jxwang@ias.edu


Curriculum Vitae

I am an assistant professor in the Department of Mathematics at Princeton University and a Veblen Fellow in the School of Mathematics at the Institute for Advanced Study.

My main areas of research are in geometry and topology. More specifically, my training was in applications of gauge theory to low-dimensional topology, while my later work has touched representation theory, algebraic combinatorics, string topology, and other parts of geometry and topology. I am also trying to think critically and proactively about AI and mathematics.



Research

  1. Link homology and loop homology

    preprint | arXiv

  2. The minimal Rickard complexes of braids on two strands

    preprint | arXiv

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

    with William Ballinger, Eugene Gorsky, and Matthew Hogancamp

    preprint | arXiv

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

    with Onkar Singh Gujral

    Algebraic and Geometric Topology 25: 4073-4075 (2025) | arXiv

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

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

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

    Advances in Mathematics 474 (2025) 110314 | arXiv

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

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

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

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

  9. Link Floer homology also detects split links

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

  10. The cosmetic crossing conjecture for split links

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

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

    with Timothy Ratigan and Luya Wang

    Journal of Knot Theory and Its Ramifications 34(11): 2550054 (2025) | arXiv



Teaching and Mentoring

Courses at Princeton

Spring 2027 - MAT 218: Multivariable Analysis and Linear Algebra II

Fall 2026 - MAT 216: Multivariable Analysis and Linear Algebra I

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 four undergraduates in the research project in knot theory this summer.

I mentored a high school research project through MIT PRIMES during 2024.



Exposition

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