The focus of Professor Holm's research is symplectic geometry and its relationships with combinatorics, algebraic topology, and algebraic geometry.
Recent projects include: (1) studying real loci of symplectic manifolds and the corresponding varieties in real algebraic geometry; and (2) investigating the topology of symplectic quotients that are orbifolds.
Extended hyperbolic surfaces in R^3; in the Ludmilla Keldysh Memorial Volume, Proceedings of the Steklov Institute of Mathematics, Vol. 247, 2004, pp.1–13.
Numerous mathematical descriptions and educational modules (some jointly with Daina Taimina) for KMODDL: Kinematic Models for Design – Digital Library; part of the National Science Digital Library, 2004-2005. http://kmoddl.library.cornell.edu/
Experiencing Geometry: Euclidean and Non-Euclidean With History (with Daina Taimina), 3rd Edition, Pearson Prentice-Hall, 2005. (pp: xxx + 402)
How to use history to clarify common confusions in geometry (with Daina Taimina); Chapter 6 in From Calculus to Computers: Using Recent History in the Teaching of Mathematics (A. Shell and D. Jardine, eds.), MAA Notes 68, 2005, pp. 57–73.
Non-Euclidean geometry (with Daina Taimina) and Differential geometry, signed articles in Encyclopedia Britannica, 2005.
Differential Geometry: A Geometric Introduction, Cornell Custom Publishing, Revised Second Edition, 2005; and Self Study Edition, 2006.
Experiencing Meanings in Geometry (with Daina Taimina); Chapter 3 in Aesthetics and Mathematics (David Pimm and N. Sinclair, eds.), Springer-Verlag, 2006, pp. 58–83.
Alive mathematical reasoning; a chapter in Educational Transformations: Changing our lives through mathematics; A tribute to Stephen Ira Brown (L. Copes and F. Rosamond, eds.), Bloomington, Indiana: AuthorHouse, 2006, pp. 247–270.