My research centers around the intersection of representation theory and low-dimensional topology, and includes objects such as Hecke algebras, Hall algebras, character varieties, and knot invariants. For some context and a few more details see my research page, or for many more details, see the papers below.


  1. Hall algebras and the Fukaya category, I.
    arXiv (with B. Cooper)
    (submitted.) (63 pages.)
  2. Affine cubic surfaces and character varieties of knots.
    arXiv (with Y. Berest)
    (Submitted) (30 pages.)
  3. The elliptic Hall algebra and the deformed Khovanov Heisenberg category.
    arXiv (with S. Cautis, A. Lauda, A. Licata, J. Sussan)
    (Submitted) (49 pages.)
  4. The HOMFLYPT skein algebra of the torus and the elliptic Hall algebra.
    Mathscinet arXiv (with H. Morton)
    (Duke, 166 (2017) no. 5.) (49 pages.)
  5. Iterated torus knots and double affine Hecke algebras.
    DOI arXiv
    (IMRN, 2017) (29 pages.)
  6. Double affine Hecke algebras and generalized Jones polynomials.
    Mathscinet arXiv (with Y. Berest)
    (Compositio 152 (2016), no. 7.) (51 pages.)
  7. Character algebras of decorated SL_2(C)-local systems.
    MathSciNet arXiv (with G. Muller.)
    (Algebr. Geom. Topol. 13 (2013) no. 4.) (40 pages.)
  8. Rational Cherednik alegbras and quasi-invariants of complex reflection groups.
    MathSciNet arXiv (with Y. Berest.) (22 pages.)
    (Mathematical aspects of quantization, Contemp. Math. 583, AMS, 2012.)
  9. On CAT(0) structures for free-by-cyclic groups
    (Topology Appl. 153 (2006) no. 15.) (10 pages.)