Research

I work on problems in the field of Algebraic Geometry. My recent projects are focussed on applications of
algebraic geometry to non-convex optimization.
Publications

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.

Undergraduate Thesis

Here is my undergraduate thesis.
Notes

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.

Student Algebraic Geometry Seminar

SAGS, 2015 Spring
Programming

Sports Tracking
Here is a demo of a system I built with Senthil Ghandi that tracks the absolute coordinates of soccer
players using broadcast video.

Ray Tracer
An easy to use light weight ray tracer.

Turing Machine
A turing machine made out of popsicle sticks and plastic bottles.