Inspired by recent work on refraction billiards in dynamics, we introduce a notion of
refraction for combinatorial billiards. This allows us to define a generalization of toric …

In our companion paper, we develop a new $ SL_4 $-web basis. Basis elements are given
by certain planar graphs and are constructed so that important algebraic operations can be …

For any non-zero complex number $ q $, excluding finitely many roots of unity of small order,
a linear basis for the $\mathrm {SL}(n) $ skein algebra of the twice punctured sphere is …

Webs are certain planar diagrams embedded in disks. They index and describe bases of
tensor products of representations of $\mathfrak {sl} _2 $ and $\mathfrak {sl} _3 $. There are …

Fraser, Patrias, Pechenik, and Striker introduced jellyfish invariants living within the flamingo
Specht module $ S^{(d^ r, 1^{n-rd})} $ indexed by ordered set partitions of $ n $ with $ d …

A web basis of a representation of 𝔖 n is a basis of the representation for which the action of
𝔖 n can be understood through combinatorial rules called skein relations. In this thesis, we …

We introduce hourglass plabic graphs and prove that certain of these graphs index a
rotationinvariant SL4-web basis, a structure that has been sought since Kuperberg's …