Joshua X. Wang
Joshua X. Wang
Office: Science Center 425a
Email: jxwang@math.harvard.edu
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.
The Gysin sequence and the sl(N) homology of T(2,m)
preprint | arXiv
Colored sl(N) homology and SU(N) representations of the trefoil
preprint | arXiv
Split link detection for sl(P) link homology in characteristic P
Journal of Topology, under revision | arXiv
On sl(N) link homology with mod N coefficients
Quantum Topology, accepted | arXiv
Link Floer homology also detects split links
Bulletin of the London Mathematical Society 53 (4): 1037-1044 (2021) | arXiv
The cosmetic crossing conjecture for split links
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
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
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.