# Publications

Filter by type:
. Poincare polynomials of character varieties, Macdonald polynomials and affine Springer fibers. arXiv preprint arXiv:1710.04513, accepted in Ann. of Math., 2020.

. Poincaré polynomials of moduli spaces of Higgs bundles and character varieties (no punctures). Invent. Math. DOI: 10.1007/s00222-020-00950-1, 2020.

. Torus link homology. arXiv preprint arXiv:1909.00418, 2019.

. The Tutte polynomial and toric Nakajima quiver varieties. arXiv preprint arXiv:1910.01633, 2019.

. The $A_{q,t}$ algebra and parabolic flag Hilbert schemes. Math. Ann. DOI: 10.1007/s00208-019-01898-1, 2019.

. Serre duality for Khovanov-Rozansky homology. Selecta Math. (N.S.) 25 (2019), no. 5, Art. 79, 33 pp., 2019.

. Rationality proofs by curve counting. Experimental Mathematics DOI: 10.1080/10586458.2019.1691088, 2019.

. On quantum cohomology of Grassmannians of isotropic lines, unfoldings of $A_n$-singularities, and Lefschetz exceptional collections. Ann. Inst. Fourier (Grenoble) 69 (2019), no. 3, 955–991, 2019.

. Elliptic dilogarithms and parallel lines. J. Number Theory 204 (2019), 1–24, 2019.

. Cell decompositions of character varieties. arXiv preprint arXiv:1905.10685, 2019.

. $\mathbb{Z}R$ and rings of Witt vectors $W_S(R)$. Rend. Semin. Mat. Univ. Padova 142 (2019), 93–102, 2019.

. Five-term relation and Macdonald polynomials. J. Combin. Theory Ser. A 163 (2019), 182–194, 2018.

. Integrality of Hausel–Letellier–Villegas kernels. Duke Math. J. 167 (2018), no. 17, 3171–3205, 2018.

. There is no strongly regular graph with parameters (460, 153, 32, 60). Contemporary computational mathematics—a celebration of the 80th birthday of Ian Sloan. Vol. 1, 2, 131–134, Springer, Cham, 2018, 2018.

. Mirror symmetry with branes by equivariant Verlinde formulae. Geometry and Physics: Volume I: A Festschrift in honour of Nigel Hitchin 189–218, Oxford Univ. Press, Oxford, 2018.

. A proof of the shuffle conjecture. J. Amer. Math. Soc. 31 (2018), no. 3, 661–697, 2017.

. Homology of torus knots. arXiv preprint arXiv:1704.07630, 2017.

. Toric braids and $(m, n)$-parking functions. arXiv preprint arXiv:1604.07456, 2016.

. Plethystic identities and mixed Hodge structures of character varieties. arXiv preprint arXiv:1603.00193, 2016.

. Finite hypergeometric functions. Pure Appl. Math. Q. 11 (2015), no. 4, 559–589, 2015.

. Dwork's congruences for the constant terms of powers of a Laurent polynomial. Int. J. Number Theory 12 (2016), no. 2, 313–321, 2015.

. Update on quantum cohomology of IG (2, 2n). arXiv preprint arXiv:1510.07903, 2015.

. Derived categories of Keum's fake projective planes. Adv. Math. 278 (2015), 238–253, 2015.

. Dubrovin's conjecture for IG(2,6). Int. Math. Res. Not. IMRN 2015, no. 18, 8847–8859, 2014.

. Gamma structures and Gauss's contiguity. J. Geom. Phys. 78 (2014), 12–18, 2014.

. Convolution bootstrap percolation models, Markov-type stochastic processes, and mock theta functions. Int. Math. Res. Not. IMRN 2013, no. 5, 971–1013, 2012.

. Joyce invariants for K3 surfaces and mock theta functions. Commun. Number Theory Phys. 3 (2009), no. 4, 655–676, 2009.

. Higher Green's functions for modular forms. arXiv preprint arXiv:0804.3184, 2008.

. Algebras Generated by Linearly Dependent Elements with Prescribed Spectra. Funct. Anal. Appl. 39 (2005), no. 3, 175–186, 2005.

. When Is a Sum of Partial Reflections Equal to a Scalar Operator. Funct. Anal. Appl. 38 (2004), no. 2, 157–160, 2004.

. On $*$-representations of algebras of Temperley-Lieb type and algebras generated by linearly dependent generators with given spectra. Proc. Inst. Math. NAS of Ukraine 50, Part 1, 2, 3, 1139–1144, 2004.

. The case where the sum of three partial reflections is equal to zero. Ukrainian Math. J. 55 (2003), no. 9, 1542–1550, 2003.

. Stochastic integral of Skorokhod type with respect to random measures. Theory Stoch. Process. vol. 7, no. 23 (3-4), 2001.