Research grants

• 2023-2026: Quivers in quantum symmetry: a path algebra framework for algebras in tensor categories. NSF award DMS-2303334. Ryan Kinser (PI). ($298,003)
• 2019-present: Quiver representations across geometry and algebra: equivariant K-theory, moduli spaces, and tensor categories. Simons Foundation Award ID: 636534. Ryan Kinser (PI). ($42,000)
• Jan 2012-Dec 2014: Quiver Representations: Algebra, Geometry, and Combinatorics. NSA Young Investigator Grant H98230-12-0244 . Ryan Kinser (PI). ($39,399)

Education grants

• 2024-2027: Graduate Assistance in Areas of National Need (GAANN), Mathematics. Department of Education grant. Ryan Kinser (Project Director), Isabel Darcy (Co-Director), Cynthia Farthing (Co-Director), Xiaoyi Zhang (Co-Director). ($840,765)
• 2021-2025: Recruiting and Training Community College and University Students to Become Culturally Responsive and Proficient Mathematics Teachers in Iowa. NSF DUE-1852725.  Dae Hong (PI), Patsy Steffen (Co-PI), Ryan Kinser (Co-PI), Julie Hartzler (Co-PI), Gregory Beaudine (Co-PI). ($1,233,606)

Conference grants

• 2016-2019: Two NSF grants funding Conference on Geometric Methods in Representation Theory, Ryan Kinser (PI), Frauke Bleher (Co-PI). (~$23,000)

• (with Elise Askelsen) "Actions of Hopf-Ore Extensions of Group Algebras on Path Algebras of Quivers", accepted to Journal of Pure and Applied Algebra, preprint arXiv:2410.14880
• (with Martina Lanini and Jenna Rajchgot) "Equivariant geometry of symmetric quiver orbit closures", submitted, preprint arXiv:2410.06929
• (with Yari Diaz and Cody Gilbert) "Total stability and Auslander-Reiten theory for Dynkin quivers", submitted, preprint arXiv:2208:02445
• (with Danny Lara) "On algebras of finite general representation type", Transformation Groups 30, 775–801 (2025), 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

It is possible i never get around to putting anything here (RK 2026-06-06)