Joshua X. Wang
Joshua X. Wang
Office: 2-252B
Email: joshuaxw@mit.edu
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
A minimality property for knots without Khovanov 2-torsion
with Onkar Singh Gujral
preprint | arXiv
The Gysin sequence and the sl(N) homology of T(2,m)
Proceedings for "Frontiers in Geometry and Topology", accepted | arXiv
Colored sl(N) homology and SU(N) representations I: the trefoil and the Hopf link
preprint | arXiv
Split link detection for sl(P) link homology in characteristic P
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 (Ph.D. requirement) - Hodge theory for matroids
The Graduate School of Arts and Sciences at Harvard presented me with the Derek C. Bok Award!
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.