[79] Automata and one-dimensional TQFTs with defects, (with Paul Gustafson, Mee Seong Im, Remy Kaldawy and Zachary Lihn), arXiv:2301.00700.

[78] One-dimensional theories with defects: the linear case, (with Mee Seong Im), arXiv:2210.00371.

[77] Odd two-variable Soergel bimodules and Rouquier complexes, (with Krzysztof Putyra and Pedro Vaz), arXiv:2205.12794.

[76] Topological theories and automata, (with Mee Seong Im), arXiv:2202.13398.

[75] Categorical lifting of the Jones polynomial: a survey, (with Robert Lipshitz), arXiv:2202.02473.

[74] Monoidal categories, representation gap and cryptography, (with Maithreya Sitaraman and Daniel Tubbenhauer), arXiv:2201.01805.

[73] Foams, iterated wreath products, field extensions and Sylvester sums (with Mee Seong Im), arXiv:2107.07845.

[72] Anchored foams and annular homology (with Rostislav Akhmechet), arXiv:2105.00921.

[71] Planar diagrammatics of self-adjoint functors and recognizable tree series (with Robert Laugwitz), arXiv:2104.01417.

[70] Two-dimensional topological theories, rational functions and their tensor envelopes (with Victor Ostrik and Yakov Kononov), arXiv:2011.14758.

[69] Conical SL(3) foams (with Louis-Hadrien Robert), arXiv:2011.11077.

[68] Decorated one-dimensional cobordisms and tensor envelopes of noncommutative recognizable power series, arXiv:2010.05730.

[67] Evaluating thin flat surfaces
(with You Qi and
Lev Rozansky),
* Communications in Mathematical Physics* 385 (2021), 1835–1870,
arXiv:2009.01384.

[66] Bilinear pairings on two-dimensional cobordisms and generalizations of the Deligne category (with Radmila Sazdanovic), arXiv:2007.11640.

[65] Universal construction of topological theories in two dimensions, arXiv:2007.03361.

[64] Link homology and Frobenius extensions II,
(with Louis-Hadrien Robert), to
appear in *Fundamenta Mathematicae*,
arXiv:2005.08048.

[63] A deformation of Robert-Wagner foam evaluation and link homology (with Nitu Kitchloo), arXiv:2004.14197.

[62] Diagrammatic categorification of the Chebyshev
polynomials of the second kind
(with Radmila Sazdanovic),

*Journal of Pure and Applied Algebra* 225, is.6, June 2021, 106592,
arXiv:2003.11664.

[61]
A faithful braid group action
on the stable category of tricomplexes
(with You Qi),

SIGMA (Symm. Integr. Geom. Methods Appl.) 16 (2020), 019, 32 pages,
arXiv:1911.02503.

[60]
Foam evaluation and Kronheimer--Mrowka theories
(with Louis-Hadrien Robert),
*Advances in Mathematics* 376 (2021), 107433,
arXiv:1808.09662.

[59] Braid group actions from categorical
symmetric Howe duality on deformed Webster algebras,

(with Aaron D. Lauda,
Joshua Sussan, and
Yasuyoshi Yonezawa),
to appear in *Transformation groups*,
arXiv:1802.05358.

[58]
Towards functor exponentiation,
(with Yin Tian),
* Journal of Algebra* 505 (2017),
arXiv:1712.02208.

[57] p-DG cyclotomic nilHecke algebras (with You Qi and Joshua Sussan), arXiv:1711.07159.

[56] How to categorify the ring of integers localized at two,
(with Yin Tian),
*Quantum Topology* 10, is.4 (2019), 723–775,
arXiv:1702.07466.

[55] The Soergel category and the redotted Webster
algebra
(with Joshua Sussan),
*Journal of Pure and Applied Algebra* 222, is.8, August 2018, 1957-2000,
arXiv:1605.02678.

[54] Linearization and categorification, arXiv:1603.08223.

[53] A categorification of the positive half of quantum gl(m|1) (with Joshua Sussan), Transactions of the AMS 369 no.3 (2017), 1627-1664, arXiv:1406.1676.

[52] Positive half of the Witt algebra acts
on triply graded link homology
(with Lev Rozansky),
*Quantum Topology* 7, no.4 (2016), 737-795,
arXiv:1305.1642.

[51] An approach to categorification of
small quantum groups
(with You Qi),
* Quantum Topology* 6, no.2 (2015), 185-311,
arXiv:1208.0616.

[50] The odd nilHecke algebra and its diagrammatics (with
Alexander Ellis and
Aaron Lauda),
*Int. Math. Research Notices* v.2014, no.4 (2014), 991-1062,
arXiv:1111.1320.

[49] The Hopf algebra of odd symmetric functions (with
Alexander Ellis),
*Advances in Math.* 231, no.2 (2012), 965-999,
arXiv:1107.5610.

[48] Categorification of the polynomial ring (with
Radmila Sazdanovic),
*Fundamenta Mathematicae* 230, no.3 (2015), 251-280,
arXiv:1101.0293.

[47] Heisenberg algebra and a graphical calculus, *Fundamenta Mathematicae* 225, (2014), 169-210,
arXiv:1009.3295.

[46] Categorifications from planar diagrammatics,
* Japanese J. of Mathematics* 5, 153--181 (2010),
arXiv:1008.5084.

[45] A categorification of the Casimir of quantum sl(2)
(with Anna Beliakova and
Aaron Lauda),
* Advances in Math.* 230, is.3 (2012), 1442-1501,
arXiv:1008.0370.

[44] How to categorify one-half of quantum gl(1|2),
*Banach Center Publications* 103, Pt.3: Khots in Poland III (2014), 211-232,
arXiv:1007.3517.

[43] Extended graphical calculus for
categorified quantum sl(2) (with
Aaron Lauda,
Marco Mackaay, and Marko Stosic), * Memoirs of the AMS* 219, no.1029 (2012),
arXiv:1006.2866.

[42] Diagrammatics for Soergel cattegories
(with Ben Elias), *Int. J. Math. Math. Sci.* (2010) Article 978635,
arXiv:0902.4700.

[41]
A diagrammatic approach to categorification of quantum groups III (with
Aaron Lauda),
*Quantum Topology* 1, is.1 (2010), 1-92,
arXiv:0807.3250.

[40]
A diagrammatic approach to categorification of quantum groups II (with
Aaron Lauda), *Trans. Amer. Math. Soc.* 363 (2011), 2685-2700,
arXiv:0804.2080.

[39]
Notes on link homology (with
Marta Asaeda), in *Low-Dimensional Topology*, ed. T.Mrowka and P.Ozsvath, IAS/Park City Mathematics Series, 139-196, 2009,
arXiv:0804.1279.

[38]
A diagrammatic approach to categorification of quantum groups I (with
Aaron Lauda), *Representation Theory* 13 (2009), 309-347,
arXiv:0803.4121.

[37]
A brief review of abelian categorifications (with
Volodymyr Mazorchuk
and Catharina Stroppel), *Theory and Applications of Categories* 22, n.19 (2009), 479-508,
arXiv:math.RT/0702746.

[36] Virtual crossings, convolutions and a categorification of the SO(2N) Kauffman polynomial (with Lev Rozansky), Journal of G�kova Geometry Topology 1 (2007), 116-214, arXiv:math.QA/0701333.

[35] An invariant of tangle cobordisms via subquotients of arc rings (with Yanfeng Chen), arXiv:math.QA/0610054.

[34]
Braid cobordisms, triangulated categories, and flag varieties (with
Richard Thomas), * Homology, Homotopy and Applications*
9 (2007), 19--94,
arXiv:math.QA/0609335.

[33]
A categorification of integral Specht modules (with
Volodymyr Mazorchuk
and Catharina Stroppel),
* Proceedings of the AMS,* vol.136, no.4 (2008), 1163-1169,
arXiv:math.RT/0607630.

[32]
Link homology and categorification, * Proceedings of the ICM-2006, Madrid,*
vol.2 989--999,
arXiv:math.QA/0605339.

[31]
A categorification of finite-dimensional irreducible representations of
quantum sl(2) and their tensor products (with Igor Frenkel
and Catharina Stroppel),
* Selecta Mathematica,* vol.12, n.3-4 (2006), 379-431,
arXiv:math.QA/0511467.

[30]
Triply-graded link homology and Hochschild homology of Soergel bimodules,
* International Journal of Math.,* vol.18, no.8 (2007), 869-885,
arXiv:math.GT/0510265.

[29]
Hopfological algebra and categorification at a root of unity: the first steps, to
appear in *Communications in Contemporary Math.,*
arXiv:math.QA/0509083.

[28]
Matrix factorizations and link homology II
(with Lev Rozansky),
*Geometry and Topology,* vol.12 (2008), 1387-1425,
arXiv:math.QA/0505056.

[27]
Link homology and Frobenius extensions, * Fundamenta Mathematicae,*
190 (2006), 179-190,
arXiv:math.QA/0411447.

[26]
Topological Landau-Ginzburg models on a world-sheet foam
(with Lev Rozansky),
* Adv. Theor. Math. Phys.,*
vol.11, no.2 (2007), 233-259,
arXiv:hep-th/0404189.

[25]
Matrix factorizations and link homology
(with Lev Rozansky),
* Fundamenta Mathematicae,* vol.199 (2008), 1-91,
arXiv:math.QA/0401268.

[24]
Homological realization of Nakajima varieties and Weyl group actions
(with Igor Frenkel and
Olivier Schiffmann), * Compositio Mathematica*
141, n. 6 (2005) 1504-1530,
arXiv:math.QA/0311485.

[23]
sl(3) link homology I, * Algebr. Geom. Topol.* 4 (2004) 1045--1081 (electronic),
arXiv:math.QA/0304375.

[22]
Categorifications of the colored Jones polynomial,
* J. Knot theory and its Ramifications* 14 (2005) no.1, 111--130,
arXiv:math.QA/0302060.

[21]
An invariant of tangle cobordisms, * Trans. Amer. Math. Soc.* 358 (2006), 315-327,
arXiv:math.QA/0207264.

[20]
Categorification of some level two representations of sl(n) (with Stella
Huerfano), * J. Knot theory and its Ramifications* 15 (2006) no.6, 695-713,
arXiv:math.QA/0204333.

[19]
Crossingless matchings and the cohomology of (n,n) Springer varieties,
* Communications in Contemporary Math.* 6 (2004) no.2, 561--577,
arXiv:math.QA/0202110.

[18]
Patterns in knot cohomology I, * Experimental mathematics* 12 (2003) no.3, 365--374,
arXiv:math.QA/0201306.

[17]
A functor-valued invariant of tangles, *Algebr. Geom. Topol.* 2 (2002), 665--741 (electronic),
arXiv:math.QA/0103190.

[16]
Quivers, Floer cohomology, and braid group actions
(with Paul Seidel),
*J. Amer. Math. Soc.* 15 (2002), no. 1, 203--271 (electronic),
arXiv:math.QA/0006056.

[15]
A categorification of the Temperley-Lieb algebra and Schur quotients of U(sl(2))
via projective and Zuckerman functors

(with Joseph Bernstein and
Igor Frenkel),
*Selecta Math. (N.S.)* 5 (1999), no. 2, 199--241,
arXiv:math.QA/0002087.

[14]
A category for the adjoint representation (with Stella Huerfano),
* J. Algebra* 246 (2001), no. 2, 514--542,
arXiv:math.QA/0002060.

[13]
A categorification of the Jones polynomial, *Duke Math. J.* 101 (2000), no. 3, 359--426,
arXiv:math.QA/9908171.

[12]
NilCoxeter algebras categorify the Weyl algebra,
* Comm. Algebra* 29 (2001), no. 11, 5033--5052,
arXiv:math.RT/9906166.

[11]
Web bases for sl(3) are not dual canonical
(with Greg Kuperberg),
*Pacific J. Math.* 188 (1999), no. 1, 129--153,
arXiv:q-alg/9712046.

[10]
Kazhdan-Lusztig polynomials and canonical basis (with Igor Frenkel
and Alexander Kirillov Jr),
* Transform. Groups* 3 (1998), no. 4, 321--336,
arXiv:q-alg/9709042.

[9] Graphical calculus, canonical bases and Kazhdan-Lusztig theory, PhD thesis, Yale University, May 1997.

[8]
Canonical bases in tensor products and graphical calculus for U_{q}(sl_{2})
(with Igor Frenkel), * Duke Math. J.* 87 (1997)
no.3, 409--480.

[7]
Doodle
groups, *Trans. Amer. Math. Soc.* 349 (1997), no. 6, 2297--2315.

[6]
Real K(π,1) arrangements from finite root systems,
* Math. Res. Lett.* 3 (1996), no. 2, 261--274.

[5]
Some remarks on Tabachnikov's invariants of plane curves. *J. Knot Theory Ramifications*
5 (1996), no. 6, 849--857.

[4]
Representations of tensor categories and Dynkin diagrams (with
Pavel Etingof),
* Internat. Math. Res. Notices* (1995) no.5, 235--247.
arXiv:hep-th/9408078.

[3] The set of slice doodles is NP-complete, preprint 1995.

[2] Surfaces in three-space and braided algebras, preprint 1995.

[1] New geometrical constructions in low-dimensional topology, preprint 1990.