About

Me. I am a postdoctoral scholar in the algebra group at the University of Kentucky. I work with Uwe Nagel on problems in computational commutative algebra. I will be on the job market in Fall 2019. Here is my CV.

Research

  1. Minimal resolutions for modules over polynomial OI-algebras.
    With Uwe Nagel. In Preparation.

  2. Gröbner bases and the Cohen-Macaulay property of Li's double determinantal varieties.
    With Patricia Klein. Submitted.

  3. Topological Complexity of Graphic Arrangements.
    Topological complexity and related topics, vol. 702 of Contemp. Math., Amer. Math. Soc., Providence, RI, 2018, pp. 121-132.

  4. Polynomial Interpolation in Higher Dimensions: From Simplicial Complexes to GC Sets.
    With Hal Schenck.
    SIAM Journal of Numerical Analysis, 55 (2017), 131-143.

  5. Classification of Groups with Strong Symmetric Genus up to Twenty-Five.
    With Tova Lindberg, Tyler London, Holden Tran, Haokun Xu.
    Houston journal of mathematics 39(1) · March 2011.

Teaching

  • Fall 2019
  • Spring 2019
    • MA 362 - Abstract Algebra II. (Archive of course materials - 4.5 MB).
    • MA 765 - Computational Commutative Algebra (Notes)
  • Fall 2018
    • MA 361 - Abstract Algebra I. (Archive of course materials - 4.4 MB)
  • Spring 2018
    • MA 261 - Introduction to Number Theory. (Archive of course materials - 3.6 MB)
  • Fall 2017
    • MA 109 - College Algebra.
    • MA 138 - Calculus II for the Life Sciences.

Other

From Fall 2017 until Spring 2019, I was the organizer of the Kentucky Algebra Seminar. In Fall 2019, the seminar organizer will be Max Kutler.

During Fall 2018 - Spring 2019, I led an undergraduate research project through the Kentucky Geometry Lab. We looked at the persistent homology of point clouds generated by noise functions, similar to those used to procedurally random generate terrain in video games.

A visual representation of a composition series for S_4 I made a visual representation of a flag of normal subgroups in the symmetric group \(S_4\), shown to the right. The \(24\times 24\) grid is a multiplication table for the group, where the group elements have been colored so as to reflect the composition series \((1) \trianglelefteq V \trianglelefteq A_4\ \trianglelefteq S_4\). A physical quilt modeled after this design is a future project of the lab's 2D visualization group.

A 3D-printed model of the Clebsch diagonal cubic, emphasizing the 27 lines Shown at left is a 3D-printed model of the Clebsch diagonal cubic which emphasized the \(27\) straight lines that it contains. Working with UKY undergraduate Sean Grate, this model was created using Sage, made suitable for printing via Blender, and printed on the Form 2 3D printer at the UK Math Lab. For more information on the mathematics behind this object, see here or here.