CV (9/2020)
I received my Ph.D. from the University of Chicago in 2007. My thesis
was on the algebraic geometry of nilpotent orbits in semi-simple Lie
Algebras. I received an M.S. from The Ohio State University in 2001.
My masters thesis was on representations of braid groups. My undergraduate
work was done at the University of Alaska, Anchorage.
I am interested in topics in the intersection of representation theory, braid groups, and quantum algebras. I also have interests in topology, knot theory, mathematical biology, mathematical climate models, and I enjoy thinking about the ways in which mathematics appears in popular culture and non-mathematical texts.
Publications:
Temporal stability vs. community matrix measures of stability and the role of weak interactions. With Amy Downing, Claire Plunkett, Jayne Ackerman Lockhart, Shannon Schlater, and Matthew Liebold. Ecology Letters 23:10 (2020) 1468-1478. (pdf)(web)
Review of Mathematics and Cliamte by Hans Kaper and Hans Engler. The American Mathematical Monthly, 123:3 (March 2016) pp. 304-308 (JSTOR)
Challenges in promoting undergraduate research
in the mathematical sciences. With Feryal Alayont, Yuliya Babenko, and Zsuzsanna Szaniszlo. Involve, 7:3 (2014) 265-271. (web)
Polar Amplification: Is Atmospheric Heat Transport Important? With Vladimir Alexeev. Climate Dynamics, 41:2 (2013) 533-547. (pdf)(web)
Modeling the Impact of Afforestation on Global Climate: A 2-box EBM. With Sriharsha Masabathula. J. Env. Stat. 4:12 (2013). (pdf)(web)
Topologies of Identity in Serial Experiments Lain. Mechademia 7: Lines of Sight, Ed. Frenchy Lunning, Univ. of Minnesota Press (2012) 191-201.
The Big Lebowski and Mathematical Logic. The Big Lebowski and Philosophy, Ed. Peter Fosl, Wiley-Blackwell (2012) 24-36.
The Krammer-Lawrence-Bigelow Representation of the Braid Groups via U_q(sl_2). With Thomas Kerler. Adv. Math. 228 (2011) 1689-1717. (pdf)(arXiv)(web)
Soft Inheritance in the Hawk-Dove Model. With Hao Do and Yixin Liu. Proc. Midstates Conference
for Undergraduate Reseach in Computer Science and Mathematics, Denison University (2011). (pdf)(web)
Evolutionary Game Theory: The Hawk-Dove Game. Computational Science Module for Capital University (2010) <http://www.capital.edu/cs-math/>.
Preprints/Unpublished:
Bethe Ansantz for Central Arrangements of Hyperplanes. (pdf)
Symplectic Manifolds, Geometric Quantization, and Unitary Representations of Lie Groups. Chicago 2nd year Topic. (pdf)
Braid Group Representations. OSU Masters Thesis. (pdf)
Nilpotent Orbits and Hilbert Schemes. (arXiv)
Student Honors Papers:
Isaac Kochman, Investigations Into the Symmetric Group, 2018. (pdf)
Khanh Q. Le, Specializations of the Lawrence Representations of the Braid Groups at Roots of Unity, 2016. (pdf)
Nam Tran Hoang, A Recursive Formulation for the Rank-Sum Statistic used to detect Genomic Copy Number Variation, 2016. (pdf)