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. My main area of research is low-dimensional topology. More specifically, I'm interested in connections between homological knot invariants arising from Floer theory and categorification, and their application to problems in knot theory and other areas of low-dimensional topology.

Curriculum Vitae

Research

• Colored sl(N) homology and SU(N) representations of the trefoil

  preprint | arXiv

• Split link detection for sl(P) link homology in characteristic P

  preprint | arXiv

• On sl(N) link homology with mod N coefficients

  Quantum Topology, under revision | arXiv

• Link Floer homology also detects split links

  Bulletin of the London Mathematical Society (2021) | arXiv

• The cosmetic crossing conjecture for split links

  Geometry & Topology, accepted | arXiv

• A combinatorial proof of invariance of double-point enhanced grid homology
  with Timothy Ratigan and Luya Wang

  preprint | arXiv

Exposition

Minor thesis - Hodge theory for matroids

Teaching and Mentoring

Fall 2021 - Math 21a - Multivariable calculus

Tutorials

Spring 2021 - Low-dimensional manifolds - Teaching evaluations

Summer 2020 - Differential forms in algebraic topology - Teaching evaluations

Summer 2019 - Knot invariants and category theory with Morgan Opie

Directed Reading Program

I used to organize the Directed Reading Program, and I've mentored five reading projects so far.

Personal

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