Publications:
- Bordered invariants from Khovanov homology
(joint with Matthew Hogancamp and Paul Wedrich),
preprint, 58 pp. - A Kirby color for Khovanov homology
(joint with Matthew Hogancamp and Paul Wedrich), 47 pp.
To appear in Journal of the European Mathematical Society (JEMS). - 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. - Link splitting deformation of colored Khovanov–Rozansky homology
(joint with Matthew Hogancamp and Paul Wedrich), 110 pp.
To appear in Proceedings of the London Mathematical Society. - A skein relation for singular Soergel bimodules
(joint with Matthew Hogancamp and Paul Wedrich),
preprint, 34 pp. - Type C Webs
(joint with Elijah Bodish, Ben Elias, and Logan Tatham),
preprint, 45 pp. - On webs in quantum type C
(joint with Logan Tatham),
Canadian Journal of Mathematics 74(3), 793–832. - HOMFLYPT homology for links in handlebodies via type A Soergel bimodules
(joint with Daniel Tubbenhauer),
Quantum Topology, 12 (2021), no. 2, 373–410 - Categorification of the internal braid group action for quantum groups I: 2-functoriality
(joint with Michael Abram, Laffite Lamberto-Egan, and Aaron Lauda) 60 pp.
To appear in Pacific Journal of Mathematics. - Annular Evaluation and Link Homology
(joint with Hoel Queffelec and Antonio Sartori),
preprint, 47 pp. - Sutured annular Khovanov–Rozansky homology
(joint with Hoel Queffelec),
Transactions of the AMS, 370 (2018), 1285-1319 - Deformations of colored sl(n) link homologies via foams
(joint with Paul Wedrich),
Geometry and Topology, 20 (2016), no. 6, 3431–3517 - Symmetric webs, Jones–Wenzl recursions, and q-Howe duality
(joint with Daniel Tubbenhauer),
International Mathematics Research Notices, (2016) 2016 (17): 5249-5290 - 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 - 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 - 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 - 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”)
Juvenilia:
- 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. - 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
Collaborators:
- Michael Abram
- Elijah Bodish
- Ben Elias
- Matt Hogancamp
- Laffite Lamberto-Egan
- Aaron Lauda
- Hoel Queffelec
- Antonio Sartori
- Ilya Spitkovsky
- Logan Tatham
- Daniel Tubbenhauer
- Paul Wedrich