"K-polynomials of type A quiver orbit closures and lacing diagrams", in Representations of Algebras, Contemporary Mathematics, vol. 705: 99-114, 2018, preprint arXiv:1706.02333 This is an less technical overview of the article with Knutson and Rajchgot, written to a representation theory audience, which also has a more detailed running example illustrating the main constructions and proof of the K-theoretic component theorem. Correction for running example: The leftmost and rightmost lacing diagrams in Figure 5 are not K-theoretic. So in Figure 6, the bottom node and the leftmost node in the row above it should be removed; values of the Mobius function remain unchanged. Probably the computational error I made was applying the move (2.4) when the middle two dots were not consecutive in their column.
(with Chelsea Walton) "Actions of some pointed Hopf algebras on path algebras of quivers", Algebra & Number Theory, 10(1):117-154, 2016, preprint arXiv:1410.7696 Minor correction for Lemma 2.5: Main statement and proof holds. Only => of consequence holds. <= direction requires faithful G(T(n))-action, along with x not acting by 0 nor 1-g. So Example 3.13 should be shorter, and Example 7.7 should be omitted. Rest of results remain unchanged.
Rank Functors and Representation Rings of Quivers (Ph.D. thesis), University of Michigan, 2009.
This essentially a concatenation of the two papers below, improved with the benefit of hindsight, more readers, and lack of space limitations (more examples, more background, and remarks on generalizations).
Some fractals that I made as part of undergrad summer research with Estela Gavosto at the University of Kansas. These are (complex) one-dimensional slices of a (complex) two-dimensional parameter space arising from the Hénon map. The classical Mandelbrot set is, for example, one of the one-dimensional slices of this set, thus the similarity to some of these slices.