One Dimensional TTT Structures Lowengrub, Daniel. "One dimensional ttt structures." The Journal of Symbolic Logic 79.03 (2014): 748-775.

A Cancellation Theorem for Segre Classes This paper proves a theorem that allows one to compute Segre classes of a subvarieties that formally locally look like sections of a vector bundle. This theorem is applied to prove a version of the Riemann-Kempf formula for singular curves.

The Chern-Mather class of a multiview variety In this paper with Corey Harris, we calculate the Chern-Mather class of the multi-view variety defined by a collection of n cameras, and use it to show how the complexity of triangulation grows with the number of cameras.

Deformation Theory These are notes that I prepared for a talk in a Deformation Theory seminar at Berkeley, 2013. The first part proves some general results related to the obstruction element and the second part applies this to the case of abelian schemes.

Hodge Decomposition Here is a proof of the general form of the Hodge decomposition theorem for elliptic complexes. From this we deduce the the decomposition theorem for both real and complex manifolds.

Log Geometry and Toric Varieties These are notes that I prepared for a talk in a Log Geometry seminar at Berkeley, 2013. The main goal is to gove an outline of how log structures can be used to obtain a compact moduli space of toric varieties.