ArXiv versions are available for most of the articles listed below.

A complete listing of my articles, published or otherwise.

The reviews of my articles on MathSciNet.

The reviews I have written for MathSciNet.

*Harmonic cubic homogeneous polynomials such that the norm-squared of the Hessian is a multiple of the Euclidean quadratic form*. [arXiv:1905.00071].

*The commutative nonassociative algebra of metric curvature tensors*. [arXiv:1901.04012].

*Critical symplectic connections on surfaces*. Journal of Symplectic Geometry. Vol. 17, No. 6 (to appear 2019). [arXiv:1410.1468].

*Left symmetric algebras and homogeneous improper affine spheres*. Annals of Global Analysis and Geometry. Vol. 53, No. 3 (April, 2018), pp. 405-443. [arXiv:1707.08896].

*Symmetries of the space of linear symplectic connections*. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 13 (2017), 002, 30 pages.

*Remarks on symplectic sectional curvature*. Differential Geometry and its Applications. Vol. 50 (February 2017), pp. 52-70. [arXiv:1610.05898].

*Infinitesimal affine automorphisms of symplectic connections*. Journal of Geometry and Physics. Vol. 106 (2016), pp. 210-212. [arXiv:1511.09258].

*Equiaffine geometry of level sets and ruled hypersurfaces with equiaffine mean curvature zero*. Mathematische Nachrichten 290 (2017), no. 2-3, 293-320. [arXiv:1503.09108].

*Functions dividing their Hessian determinants and affine spheres*. The Asian Journal of Mathematics. Vol. 20, No. 3, pp. 503-530, July 2016. [pdf] [arXiv:1307.5394].

*A Schwarz lemma for Kähler affine metrics and the canonical potential of a proper convex cone*. Annali di Matematica Pura ed Applicata. February 2015, Vol. 194, Issue 1, pp. 1-42. [arXiv:1206.3176].

*Geometric structures modeled on affine hypersurfaces and generalizations of the Einstein Weyl and affine hypersphere equations*. Extended Abstracts Fall 2013, Research Perspectives CRM Barcelona (Trends in Mathematics), 2015, Birkäuser Basel. pp. 15-19.

*Ricci flows on surfaces related to the Einstein Weyl and Abelian vortex equations*. Glasgow Mathematical Journal. Vol. 56, Issue 03 (Sept., 2014), pp. 569-599. [pdf]

*WHAT IS … an affine sphere?*Notices of the American Mathematical Society. March 2012, Vol. 59, Issue 3. A Chinese translation (pdf) of this article is available in Mathematical Advances in Translation Vol. 35 (2), pp. 181-184. (ISSN 1003-3092).

*Einstein-like geometric structures on surfaces*. Annali della Scuola Normale Superiore, Classe di Scienze Vol. XII, issue 3 (2013) 499-585. [arXiv:1011.5723].

*Geometric structures modeled on affine hypersurfaces and generalizations of the Einstein Weyl and affine hypersphere equations*. [arXiv:0909.1897].

*Projectively invariant star products*. International Mathematics Research Papers 9 (2005), 461-510, 2005. [math.DG:0504596]. (An [erratum] clarifies some ambiguities in the exposition.)

*Contact projective structures*. Indiana University Mathematics Journal 54 (2005), 1547–1598. [math.DG:0402332]. (Note: In the statement of Theorem B, the assumption that the ambient connection is homogeneous is omitted, although it is assumed in the proof, and is necessary for the uniqueness.)

*Contact Schwarzian derivatives*. Nagoya Mathematical Journal 179 (2005), 163-187. [math.DG:0405369].

*Contact path geometries*. [math.DG:0508343]. (I intend someday to rewrite this article completely. The arXiv version contains some mostly inconsequential but potentially confusing misstatements.)