Research Interests
My research interests lie in applied differential and algebraic geometry. In particular I am interested in how geometric and algebraic tools can aide in understanding objects represented by continuous, discrete, or noisy data, such as in detecting invariant features and symmetries under groups of transformations and other equivalence relations.
Publications and Preprints

Signatures of algebraic curves via numerical algebraic geometry, preprint (Dec 2020), journal version of conference proceeding, code available here (with Tim Duff)

The moving frame method for iteratedintegrals: orthogonal invariants, preprint (Dec 2020) (with Joscha Diehl, Rosa Preiß, and Nikolas Tapia)

Numerical equality tests for rational maps and signatures of curves, Proc. of the 45th ISSAC (2020), pp. 154161, code available here (with Tim Duff)

Maximum Likelihood Degree of the Small Linear Gaussian Covariance Model, Algebraic Statistics. 11 (2020) No. 2, pp. 107123 (with Jane Ivy Coons and Orlando Marigliano)

Differential signatures of algebraic curves, SIAM J. Appl. Algebra Geom. 4, 1 (2020), 185226 (with Irina A. Kogan and Cynthia Vinzant)

Existence of positive periodic solutions for a higher order difference equations, Diff. Eq. and Dynam. Syst. 23 (2015) No. 2, pp. 389407 (with Jacob Johnson, Lingju Kong, and Alexander Ruys de Perez)

The classification and curvature of biquotients of the form Sp(3)//Sp(1) , Ann. Global Anal. Geom. 46 (2014) No. 4, pp. 389407 (with Jason DeVito, Robert DeYeso III, and Philip Wesner)

Existence of positive periodic solutions for higher order singular difference equations, Electron. J. Qual. Theory Differ. Equ. (2014) No. 3, pp. 18 (with Jacob Johnson, Lingju Kong, and Alexander Ruys de Perez)
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Other work
Links for slides and maple code
Thesis
Where you can find me
Aug. 2021  SIAM Conference on Applied Algebraic Geometry (Texas A&M)
Aug. 2020  Geometry of curves in time series and shape analysis (MPI MiS  online)
Oct. 2020  Graphical Models Workshop (TU Munich)
Sep. 2019  Macaulay2 Workshop (Universität des Saarlandes)
Apr. 2019  Meeting on Applied Algebraic Geometry (Georgia Tech)
Feb. 2019  Algebraic Vision Research Cluster at ICERM (Brown University)
Jan. 2019  Joint Mathematics Meetings (Baltimore, MD)
Fall 2018  Nonlinear Algebra at ICERM (Brown University)
June 2018  Applications of Polynomial Systems (Texas A&M)
Apr. 2018  Meeting on Applied Algebraic Geometry (Georgia Tech)