Research & Scholarship

Undergraduate Research

If you are an undergraduate student at Wake Forest interested in mathematical research, please feel free to reach out to me!

My area of expertise is the representation theory of quivers. This lives in the intersection of several fun areas of mathematics, i.e., algebra, topology, geometry, combinatorics, and mathematical physics. I would be excited to mentor research projects in any of those areas (and who knows? ... maybe more areas!)

I think a good background for working with me would be to complete the following WFU courses (but not required!):

MTH121 (or MTH205). Linear Algebra
Calculus through MTH113. Multivariable Calculus
MTH117. Discrete Math

If you have also taken (or are taking) Modern Algebra, Topology, Complex Analysis, and/or Geometry that is even better, but not at all required.

Selected Publications

J. Allman, A. Ksir, N. Hetherington III, M. Selbach-Allen, & D. Skipper. Activating Calculus to Command the Seas: Reflecting on ten years of active and inquiry-based learning at the US Naval Academy. PRIMUS, 31:3-5 (2021), 449--466
J. Allman & R. Rimányi. K-theoretic Pieri rule via iterated residues. Sém. Lothar. Combin. 80B (2018), Art. 48, 12 pp.
J. Allman. Grothendieck classes of quiver cycles as iterated residues. Michigan Math. J. 63 (2014), no. 4, 865–888.
J. Allman. Actions of finite-dimensional, non-commutative, non-cocommutative Hopf algebras on rings. MA thesis. Wake Forest University (2009)

Coauthors and collaborators (past and present)

L. Yengulalp. WFU
A. Ksir. US Naval Academy
D. Skipper. US Naval Academy
N. Hetherington III.
M. Selbach-Allen. Stanford
R. Rimányi. UNC Chapel Hill
J.E. Grabowski. Lancaster University (UK)

Undergraduate research projects advised

Lyle Huang (WFU 2022-present). Quiver Representations and Persistent Homology.
Zezhong Zhang (WFU 2020-2021). Iterated Residues and Schur Functions.
Karl Schwarzkopf (USNA 2018-2020). Quiver representations and quantum dilogarithms for the D4 Dynkin quiver.
Jacob Pittman (USNA 2017-2018). Understanding the Link Between Khovanov's Homology and the Jones Polynomial.