Research Interests
I am interested in deep learning in image processing and applications of geometry to image science, data science, and statistics. In particular I am interested in deep learning techniques in medical imaging and in how geometric and algebraic tools can aide in understanding objects represented by continuous, discrete, or noisy data.
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 iterated-integrals: 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. 154-161, code available here (with Tim Duff)
​
-
Maximum Likelihood Degree of the Small Linear Gaussian Covariance Model, Algebraic Statistics. 11 (2020) No. 2, pp. 107-123 (with Jane Ivy Coons and Orlando Marigliano)
​
-
Differential signatures of algebraic curves, SIAM J. Appl. Algebra Geom. 4, 1 (2020), 185-226 (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. 389-407 (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. 389-407 (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. 1-8 (with Jacob Johnson, Lingju Kong, and Alexander Ruys de Perez)
2
Other work
Links for slides and maple code
Thesis
Where you can find me
Nov. 2021 - Moving Frames and their Modern Applications (BIRS)
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)