# Research

Having recently reemerged in an academic setting, I’m beginning to build a research program. My past research still informs much of my interest:

- Profiling and understanding behaviors on the internet in the areas of security and abusive conduct (industry).
- Understanding symmetries of geometric systems using algebraic techniques (mathematics).

Current projects in which I’m involved, while in their beginning phases of work, support numerous undergraduate research assistants, whom I mentor (5 in the past year) as well as Senior Capstone projects.

### Scaling up Scientific Investigations

I am the “methodological mentor” for a number of cross-disciplinary projects, often supervising undergraduate Data Science students as research assistants. These projects include work with the Earth Sciences and Computational Social Sciences.

### Heterogeneous Graphs

Much of data science deals with combining heterogeneous data sources to understand a process of interest. This often leads to an incommensurability of scales, under which the choice of metric significantly affects the results. Graphs provide a natural structure on which represent this choice; the dynamics of human behavior on the internet provide many examples of such graphs.

A few specific projects in progress lie in the following areas:

- Outlier Detection on Graphs.
- Record linkage via graph clustering.
- Nonparametric graph sampling techniques.

### Pedagogy and Data Science

Work on new course development is on the curriculum page.

I have preliminary work on creating an Introduction to Data Science course, in the spirit of data8, appropriate for majors at UCSD. In particular, introducing tabular computation in python in a way that is both easily approachable by those new to coding as well as directly usable after leaving the course. This project resulted in the python package `babypandas`

available on PYPI. This project is being adopted outside of UCSD.

### Mathematics

My research as a mathematician was in the area of Symplectic and Poisson Geometry. I’ve found a few interesting connections to my current interests, including how to best design a neural-network architecture for a specified symmetry (group-action).

My mathematics preprints can be found on the ArXiV:

Extensions of Poisson Structures on Singular Hypersurfaces

On Embedding Singular Poisson Spaces (Dissertation)