I am a topologist at heart. I have been studying the graphically presented monoidal categories known as spiders or web categories. I have been working on the highest-weight projectors and the defining skein relations for web categories of different quantum groups. I have also been working on the categorification of quantum link invariants, as well as applications of web categories in algebraic combinatorics, algebraic geometry, and statistical mechanics.
Writings
In preparation:
Webs and pockets in SL(4) affine building, joint with Christian Gaetz, Jessica Striker, and Joshua P. Swanson.
Howe duality for the quantum orthogonal group, joint with Elijah Bodish and Daniel Tubbenhauer.
SL(4) foams with seams, joint with Jernej Grlj, Mikhail Khovanov, and Melissa Zhang.
Central elements in the Sp(2n) skein algebra, joint with Vijay Higgins.
Publications and preprints:
Webs and multiwebs for the symplectic group, joint with Richard Kenyon, submitted, 2024. arXiv:2411.03153.
Webs for the Quantum Orthogonal Group, joint with Elijah Bodish, submitted, 2023. arXiv:2309.03623.
Triple Clasp Formulas for G2, joint with Elijah Bodish, Quantum Topology, online, 2024. arXiv:2112.01007.
Talks
Upcoming Talks
N/A
Past Talks
Central elements in the Sp(2n) skein algebra, May 15, 2025, Lightning Talks, Links in Dimensions 3 and 4, ICERM.
SL(4) Foam Evaluation and 6-Valent Seams, May 13, 2025, Links in Dimensions 3 and 4, ICERM.
SL(4) foams and degree-6 vertex, May 3, 2025, Contributed Talks Session 1, Representation Theory of Groups and Algebras, College of Charleston.
Webs and multiwebs for the symplectic group, February 21, 2025, Friday Mornings Seminar, Yale University.
Braiding formulas for web categories of Sp(2n) and O(m), January 15, 2025, Algebra Seminar, University of Virginia.
Central elements in the Sp(2n) skein algebra, January 13, 2025, Geometry/Topology Seminar, UC Davis.
Webs and Howe duality for the quantum orthogonal group, December 6, 2024, Algebra and Representation Theory Seminar, University of Oklahoma.
Webs and Howe duality for the quantum orthogonal group, December 4, 2024, Lie Groups Seminar, Oklahoma State University.
Quantum invariants for links and 3-manifolds, December 3, 2024, Topology Seminar, Oklahoma State University.
Webs and pockets in SL(4) affine building, October 13, 2024, Short Talks Session 1, Quantum Groups and Represnetation Theory, North Carolina State University.
Webs and the determinant of the adjacency matrix of a graph, October 8, 2024, Undergraduate Mathematics Seminar, Johns Hopkins University.
Webs and pockets in SL(4) affine building, May 22, 2024, Algebraic Geometry Seminar, UC Davis.
Generalized dimer models and type C web categories, May 4, 2024, Special Session on Geometry, Integrability, Symmetry and Physics, AMS Spring Western Sectional Meeting, San Francisco State University.
Dimers and Sp(2n) webs, March 4, 2024, Participant Talks, Randomness and Lie-theoretic Structures, University of Virginia.
Webs for the Quantum Orthogonal Group, March 2, 2024, Contributed Talks Session 2, Quantum Structures in Lie Theory, University of Virginia.
Dimers and Sp(2n) webs, February 13, 2024, Algebra & Discrete Mathematics Seminar, UC Davis.
Webs for the Quantum Orthogonal Group, January 5, 2024, AMS Contributed Paper Session on Algebraic Structures, Logic, Set Theory, and Related Topics, JMM 2024.
Graphs and Representations of Quantum Groups, September 18, 2023, USC Combinatorics Seminar.
Webs and Clasps, May 24, 2023, Bilkent Topology Seminar.
Webs for quantum orthogonal group, March 13, 2023, Algebra & Discrete Mathematics Seminar, UC Davis.
Spiders and representations of quantum groups, November 16, 2022, Student-Run Research Seminar, UC Davis.
Clasp expansions for quantum g2, May 16, 2022, Algebra & Discrete Mathematics Seminar, UC Davis.
Highest weight projectors for quantum g2, March 3, 2022, Student-Run Research Seminar, UC Davis.
Activities
Organizing AMS Special Session on Recent Progress on Categorification and Quantum Groups at the AMS 2025 Spring Eastern Sectional Meeting, with Elijah Bodish, Vijay Higgins, Artem Kalmykov, and Kang Lu.
In-Person Conferences and Workshops
Upcoming
Diagrammatic Categorification, October 20-24, 2025, ICERM.
Webs in Algebra, Geometry, Topology and Combinatorics, December 8-12, 2025, ICERM.
Past
Categorification and Symplectic Duality, June 3-7, 2025, Northeastern University.
Links in Dimensions 3 and 4, May 12-16, 2025, ICERM.
15th Southeastern Lie Theory Workshop, May 2-4, 2025, College of Charleston.
AMS 2025 Spring Eastern Sectional Meeting, April 5-6, 2025, University of Connecticut, Hartford.
Quantum Groups and Representation Theory, October 12-15, 2024, North Carolina State University.
Cluster Algebra Summer School, June 17-21, 2024, University of Connecticut, Storrs.
AMS 2024 Spring Western Sectional Meeting, May 4-5, 2024, San Francisco State University.
Advances in Lie Theory, Representation Theory and Combinatorics: Inspired by the work of Georgia M. Benkart, May 1-3, 2024, SLMath.
Western Algebraic Geometry Symposium, April 27-28, 2024, University of California, Davis.
Workshop II: Integrability and Algebraic Combinatorics, April 15-19, 2024, IPAM.
Randomness and Lie-theoretic Structures, March 4-5, 2024, University of Virginia.
Quantum Structures in Lie Theory, March 1-3, 2024, University of Virginia.
2024 Joint Mathematics Meetings, January 3-6, 2024, Moscone Center, San Francisco.
FPSAC 2023 (Formal Power Series and Algebraic Combinatorics), July 17-21, 2023, University of California, Davis.
Coulomb Branches and Knot Homology, June 19-23, 2023, Massachusetts Institute of Technology.
QUACKS II (QUAntum groups, Categorification, Knot invariants, and Soergel bimodules II), August 8–12, 2022, University of Oregon.
From Representation Theory to Mathematical Physics and Back, May 31–June 4, 2022, Simons Center for Geometry and Physics.
New Developments in Quantum Topology, June 3–7, 2019, University of California, Berkeley.