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.

### Papers

- 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.

DOI arXiv

(**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

MathSciNet

(**Topology Appl.**153 (2006) no. 15.) (10 pages.)