river@math(dot)berkeley(dot)edu

Office: Evans 853

I am a fifth year graduate student in Mathematics at UC Berkeley. My research is in symplectic geometry, persistent homology, and topological data analysis.

My PhD advisor is Katrin Wehrheim. My thesis work is in polyfold theory, the natural foundation for modern symplectic topology.

More recently I have been working in persistent homology and topological data analysis with Gunnar Carlsson. We are developing the (persistent) homotopy theory of finite metric spaces. I am also applying the Mapper algorithm to analysis of real-world datasets.

Here is my CV.

1. Künneth formulas in persistent homology (joint with Gunnar Carlsson), in preparation.

2. A polyfold proof of the Arnold conjecture (joint with Katrin Wehrheim), in preparation.

3. Coherent M-polyfold theory, in preparation.

4. Counterexamples in scale calculus (joint with Zhengyi Zhou, Katrin Wehrheim), arxiv:1807.02591.

5. Polyfold regularization of constrained moduli spaces, arxiv:1807.00386.