- (with Yari Diaz and Cody Gilbert) "Total stability and Auslander-Reiten theory for Dynkin quivers", preprint arXiv:2208:02445
- (with Danny Lara) "On algebras of finite general representation type", accepted to
*Transformation Groups*, preprint arXiv:2204.02847 - (with András C. Lőrincz) "Representation varieties of algebras with nodes",
*Journal of the Institute of Mathematics of Jussieu*, Volume 21, Issue 6, November 2022, pp. 2215-2245, preprint arXiv:1810.10997 - "Total stability functions for type A quivers",
*Algebras and Representation Theory*25, 835-845 (2022), preprint arXiv:2002.12396

- (with Amrei Oswald) "Hopf actions of some quantum groups on path algebras",
*Journal of Algebra*, 587, 85-117, 2021, preprint arXiv:2010.15197 - (with Pavel Etingof and Chelsea Walton) "Tensor algebras in finite tensor categories",
*International Mathematics Research Notices*, Volume 2021, Issue 24, December 2021, Pages 18529-18572, preprint arXiv:1906.02828 - (with Jenna Rajchgot) "Type D quiver representation varieties, double Grassmannians, and symmetric varieties",
*Advances in Mathematics*, 376:107454, 44, 2021, preprint arXiv:1901.10014*In Theorem 1.1, the sentence "The image of the map is the set of orbit closures which have non-trivial intersection with U." should be removed, but does not affect the rest of the paper.* - (with Thorsten Weist) "Tree normal forms for quiver representations",
*Documenta Mathematica, 24, 1245-1294 (2019)*, preprint arXiv:1810.04977 - (with Andrew T. Carroll, Calin Chindris, and Jerzy Weyman) "Moduli spaces of representations of special biserial algebras",
*International Mathematics Research Notices*2020(2):403-421, 2020, preprint arXiv:1706.07022 - (with Allen Knutson and Jenna Rajchgot) "Three combinatorial formulas for type A quiver polynomials and K-polynomials",
*Duke Mathematical Journal*, 168(4):505-551, 2019, preprint arXiv:1503.05880 - (with Calin Chindris) "Decomposing moduli of representations of finite-dimensional algebras",
*Mathematische Annalen*372(1-2):555–580, 2018, preprint arXiv:1705.10255 - "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.* - (with Jenna Rajchgot) "Type A quiver loci and Schubert varieties",
*Journal of Commutative Algebra*7(2):265-301, 2015, preprint arXiv:1307.6261 - (with Calin Chindris and Jerzy Weyman) "Module varieties and representation type of finite-dimensional algebras",
*International Mathematics Research Notices*2015(3):631-650, 2015, preprint arXiv:1201.6422 - "Tree modules and counting polynomials",
*Algebras and Representation Theory*16(5):1333-1347, 2013, preprint arXiv:1112.4782 - (with Ralf Schiffler) "Idempotents in representation rings of quivers",
*Algebra & Number Theory*6(5):967-994, 2012, preprint arXiv:1009.0029 - "Rank Loci in Representation Spaces of Quivers", preprint arXiv:1004.1981
- "New Inequalities for Subspace Arrangements",
*Journal of Combinatorial Theory Series A*, 118(1):152-161, 2011, preprint arXiv:0905.1519 - 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).* - "Rank Functions on Rooted Tree Quivers",
*Duke Mathematical Journal*, 152(1):27-92, 2010. Preprint arXiv:0807.4496 Relevant - "The Rank of a Quiver Representation",
*Journal of Algebra*, 320(6):2363-2387, 2008. Preprint arXiv:0711.1135

- Slides of the talk Moduli spaces of representations of tame finite-dimensional algebras to accompany this video at Banff International Research Station in September 2022, which has a technical error covering parts of the slides...
- Notes from 90 minute panoramic talk
*Quiver representations and multiple flag varieties*, given at GAAG 2020, surveying joint research program with Jenna Rajchgot. - Notes from talk
*Stability conditions and Auslander-Reiten sequences*, given at IV ICRAAZ, reporting recent results of joint work with Yariana Diaz and Cody Gilbert - Notes on "Introduction to Geometry of Representations of Algebras" from CIMPA school in Medellín, Colombia, June 2018.
- Slides from Midwest Combinatorics Conference Univ. Minnesota May 2015 (similar to slides used at UNAL Encuentro de Matematicas in Bogota, summer 2014)
- Slides from Auslander conference 2015 (similar to the slides used at the AMS meeting in March 2015 at Michigan state)
- Slides from ICRA 2012 in Bielefeld on modules varieties with dense orbits in every component and generic representation theory of algebras.

**Notes from Math 5210 Introduction to Representation Theory and Lie Algebras** (University of Connecticut, Spring 2010)

Thanks to Ben Salisbury for typing these up during class (he has many more notes on his homepage). They also include some student presentations. To my knowledge, they haven't been carefully proofread.

**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.