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

**18) A Kirby color for Khovanov homology**

(joint with Matthew Hogancamp and Paul Wedrich),

*preprint*, 47 pp.

**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*, 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”*)

Once upon a time, I studied properties of the Aluthge transform. The following papers are not on the arXiv, so the journal version are linked:

**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