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