## Publications / Preprints

### Older Stuff

• The classical and arithmetic standard conjectures
Masters Thesis supervised by Christophe Soulé.

We give an introduction to intersection theory for schemes over a field, as well as intersection theory for arithmetic surfaces over $\mathrm{Spec}(\mathbb{Z})$. We give an overview of the standard conjectures, as well as the arithmetic standard conjectures.

• Graphical Display of Search Trees for Transparent Robot Programming
with Joaquin Pockels and Dave Touretzky

Search algorithms such as Rapidly-exploring Random Trees (RRTs) are common in robot programming. Including graphical representations of the output of these algorithms in a robotics framework can make the algorithms more accessible to students, and can also help programmers analyze and account for unexpected results. For this project, we used the Tekkotsu open source robot programming framework, available at Tekkotsu.org. We extended Tekkotsu’s graphical user interface for displaying both vision data and maps, to conveniently allow the user to graphically display the output of the RRT search. We created several demos using two types of searches: one from a navigation path planner, and one from an arm path planner. In some cases the search had no solution, and the graphical output helped to illustrate why. This confirms the effectiveness of the RRT visualization when explaining the unpredicted behaviors and results of the search.