My work explores structural properties of link homology and related quantum invariants, as well as connections to categorical representation theory:

17) A note on the Sundaram–Stanley bijection (or, Viennot for up-down tableaux)
(joint with Elijah Bodish, Ben Elias, and Logan Tatham),
preprint, 14 pp.

16) Link splitting deformation of colored Khovanov–Rozansky homology
(joint with Matthew Hogancamp and Paul Wedrich),
preprint, 110 pp.

15) A skein relation for singular Soergel bimodules
(joint with Matthew Hogancamp and Paul Wedrich),
preprint, 34 pp.

14) Type C Webs
(joint with Elijah Bodish, Ben Elias, and Logan Tatham),
preprint, 45 pp.

13) On webs in quantum type C
(joint with Logan Tatham),
Canadian Journal of Mathematics (published online on February 26, 2021), 38 pp.

12) HOMFLYPT homology for links in handlebodies via type A Soergel bimodules
(joint with Daniel Tubbenhauer),
Quantum Topology, 12 (2021), no. 2, 373–410

11) Categorification of the internal braid group action for quantum groups I: 2-functoriality
(joint with Michael Abram, Laffite Lamberto-Egan, and Aaron Lauda)
preprint (available upon request), 60 pp.

10) Annular Evaluation and Link Homology
(joint with Hoel Queffelec and Antonio Sartori),
preprint, 47 pp.

9) Sutured annular Khovanov–Rozansky homology
(joint with Hoel Queffelec),
Transactions of the AMS, 370 (2018), 1285-1319

8) Deformations of colored sl(n) link homologies via foams
(joint with Paul Wedrich),
Geometry and Topology, 20 (2016), no. 6, 3431–3517

7) Symmetric webs, Jones–Wenzl recursions, and q-Howe duality
(joint with Daniel Tubbenhauer),
International Mathematics Research Notices, (2016) 2016 (17): 5249-5290

6) The sl(n) foam 2-category: a combinatorial formulation of Khovanov–Rozansky homology via categorical skew-Howe duality
(joint with Hoel Queffelec),
Advances in Mathematics, 302 (2016), 1251–1339

5) Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m) 
(joint with Aaron Lauda and Hoel Queffelec),
Algebraic and Geometric Topology, 15-5 (2015), pp. 2515-2606

4) A categorification of quantum sl(3) projectors and the sl(3) Reshetikhin-Turaev invariant of tangles
Quantum Topology, 5 (2014), no. 1, pp. 1-59

3) A note on the Grothendieck group of an additive category 
Bulletin of Chelyabinsk State University, 2015. no. 3 (358). Mathematics. Mechanics. Informatics. Issue 17. pp. 135-139 (Proceedings of the International Conference “Quantum topology”)

Previously, I studied properties of the Aluthge transform:

2) On the numerical range behavior under the generalized Aluthge transform
(joint with Ilya Spitkovsky),
Linear and Multilinear Algebra, vol. 56 no. 1&2 (January, 2008), pp. 163-177.

1) On the stabilization of the Aluthge sequence
(joint with Ilya Spitkovsky),
International Journal of Information and Systems Sciences – Special Issue on Matrix Analysis and Applications, vol. 4 no. 1 (Spring, 2008), pp. 178-189