Publications

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. On Macdonald expansions of $q$-chromatic symmetric functions and the Stanley–Stembridge conjecture. J. reine angew. Math., Accepted, 2026.

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. Refined Verlinde and Segre formula for Hilbert schemes. Moduli, Accepted, 2026.

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. Coherent sheaves on surfaces, COHAs and deformed $W_{1+\infty}$-algebras. Moduli 3, e13, 2026.

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. Cohomology rings of character varieties. European Congress of Mathematics, 637–663, 2026.

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. Hard Lefschetz phenomena and Lie algebra actions in various contexts. Proceedings of the International Congress of Mathematicians 2026 4, 586–601, 2026.

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. Tautological classes for $(n,n+1)$ torus knots. Preprint, 2026.

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. A combinatorial formula for the nabla operator. Compos. Math. 161, no. 4, 800–830, 2025.

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. Toric stratifications of character varieties. Publ. Math. IHÉS 142, 153–240, 2025.

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. On the global dimension of Nakayama algebras. Preprint, 2025.

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. Symmetric and non-symmetric F-conjectures are equivalent. Preprint, 2025.

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. Tautological classes and symmetry in Khovanov–Rozansky homology. Duke Math. J. 173, no. 13, 2481–2561, 2024.

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. Automorphisms and deformations of regular semisimple Hessenberg varieties. Preprint, 2024.

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. Type $A$ DAHA and doubly periodic tableaux. Adv. Math. 416, 108919, 2023.

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. A proof of the compositional Delta conjecture. Adv. Math. 402, 108342, 2022.

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. Homology of torus knots. Geom. Topol. 26, no. 1, 47–70, 2022.

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. Rationality proofs by curve counting. Exp. Math. 31, no. 3, 773–782, 2022.

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. The Tutte polynomial and toric Nakajima quiver varieties. Proc. Roy. Soc. Edinburgh Sect. A 152, no. 5, 1323–1339, 2022.

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. $P=W$ via $\mathcal{H}_2$. Preprint, 2022.

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. Toric braids and $(m,n)$-parking functions. Duke Math. J. 170, no. 18, 4123–4169, 2021.

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. GKM spaces, and the signed positivity of the nabla operator. Preprint, 2021.

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. Non-abelian Abel's theorems and quaternionic rotation. Preprint, 2021.

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. Poincaré polynomials of character varieties, Macdonald polynomials and affine Springer fibers. Ann. of Math. (2) 192, no. 1, 165–228, 2020.

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. Poincaré polynomials of moduli spaces of Higgs bundles and character varieties (no punctures). Invent. Math. 221, no. 1, 301–327, 2020.

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. The $A_{q,t}$ algebra and parabolic flag Hilbert schemes. Math. Ann. 376, no. 3–4, 1303–1336, 2020.

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

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. $ZR$ and rings of Witt vectors $W_S(R)$. Rend. Semin. Mat. Univ. Padova 142, 93–102, 2019.

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

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

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

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. Torus link homology. Preprint, 2019.

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

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

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

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. There is no strongly regular graph with parameters (460,153, 32, 60). Contemporary Computational Mathematics - a celebration of the 80th birthday of Ian Sloan, 2018.

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. Dwork's congruences for the constant terms of powers of a Laurent polynomial. Int. J. Number Theory 12, no. 2, 2016.

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. Plethystic identities and mixed Hodge structures of character varieties. Preprint, 2016.

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

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

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

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. Update on quantum cohomology of IG (2, 2n). Preprint, 2015.

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

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

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

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. Higher Green's functions for modular forms. Preprint, 2008.

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

DOI Full text (Russian)

. Certain Examples of Deformed Preprojective Algebras and Geometry of Their $*$-Representations. Preprint, 2005.

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. Kleinian singularities and algebras generated by elements that have given spectra and satisfy a scalar sum relation. Algebra Discrete Math. 2004, no. 3, 89–110, 2004.

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. 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, 1139–1144, 2004.

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. When is a sum of partial reflections equal to a scalar operator?. Funct. Anal. Appl. 38, no. 2, 157–160, 2004.

DOI Full text (Russian)

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

DOI Full text (Russian)

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