I am a researcher in applied algebraic geometry. My research is
focused on numerical methods and algorithms for invariants of
algebraic varieties. I'm also interested in applications, for example
to the kinematics of mechanisms and computational chemistry.
Papers and preprints
"The numerical algebraic geometry of bottlenecks" (submitted).
S. Di Rocco, D. Eklund, C. Peterson,
"Numerical polar calculus and cohomology of line bundles" (to appear in Advances in Applied Mathematics).
"Curves on Heisenberg invariant quartic surfaces in
projective 3-space" (to appear in European Journal of Mathematics).
H. Abo, D. Eklund, T. Kahle, C. Peterson,
"Eigenschemes and the Jordan canonical form",
Linear Algebra and its Applications, Volume 496, 121-151 (2016).
D. Bates, B. Davis, D. Eklund, E. Hanson, C. Peterson,
"Perturbed homotopies for
finding all isolated solutions of polynomial systems",
Applied Mathematics and Computation, Volume 247, 301-311 (2014).
D. Bates, D. Eklund, C. Peterson,
"Computing intersection numbers of Chern classes",
Journal of Symbolic Computation, Volume 50, 493-507 (2013).
D. Eklund, C. Jost, C. Peterson,
"A method to compute Segre classes of subschemes of projective space",
Journal of Algebra and Its Applications Volume 12, Number 2 (2013).
S. Di Rocco, D. Eklund, C. Peterson, A. Sommese,
"Chern numbers of smooth varieties via homotopy continuation and intersection theory",
Journal of Symbolic Computation, Volume 46, Issue 1 (2011).
S. Di Rocco, D. Eklund, A. Sommese, C. Wampler,
"Algebraic C*-actions and the inverse kinematics of a general 6R manipulator",
Applied Mathematics and Computation, Volume 216, Issue 9, 2512-2524 (2010).
Class in applied algebraic
geometry (spring 2017)
Some small examples in Bertini: