• Spin link homology, joint with Ben Elias and David Rose

• Orthogonal Howe duality and dynamical (split) symmetric pairs, joint with Artem Kalmykov (Submitted)

• Orthogonal webs and semisimplification, joint with Daniel Tubbenhauer (Submitted)

• Webs for the quantum orthogonal group, joint with Haihan Wu (Submitted)

• On a symplectic quantum Howe duality, joint with Daniel Tubbenhauer (Submitted)

• Triple clasp formulas for G2, joint with Haihan Wu (Quantum Topology)

• A Note on the Stanley-Sundaram bijection, joint with Ben Elias, David Rose, and Logan Tatham (Submitted)

• Type C Webs, joint with Ben Elias, David Rose, and Logan Tatham (Submitted)

• Triple Clasp Formulas for C2 Webs (Code) (Journal of Algebra)

• Web Calculus and Tilting Modules in Type C2 (Quantum Topology)

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• University of Oregon - Dissertation 

I am actively working on problems related to.

• Generators and relations for Rep(G) (i.e. webs). 

• Spin_{2n+1} link homology (folding type A foams).

• Categorified Spin_{2n}-O(m) Howe duality. 

• Semisimplification of monoidal categories appearing in modular representation theory of reductive groups.

• Dynamical iquantum groups. 

• Drinfeld-Kohno theorem for iquantum Weyl groups.

• Elias's clasp conjecture.

Some things I want to someday understand.

• K-theory and quantum Satake.

• Knot homology.

• Geometry of the Nilpotent Cone (especially the relationship to cell theory: Lusztig--Vogan bijection, perverse coherent sheaves).

• Geometric representation theory approach to Sp(V)-SL(2) Howe duality.

• Koszul Duality (how to use Soergel modules to study category O).

• Representation theory of real reductive groups (Lusztig Vogan module: D^K(G/B)).

• Modular representation theory of finite groups.