Benjamin Filippenko
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.



Publications and preprints

Topological Data Analysis:

1. G. Carlsson, B. Filippenko, Künneth formulas in persistent homology, in preparation.


Symplectic Topology:

1. B. Filippenko, K. Wehrheim, A polyfold proof of the Arnold conjecture, arxiv:1810.06180 (October 2018).

2. B. Filippenko, Coherent M-polyfold theory, in preparation.

3. B. Filippenko, Z. Zhou, K. Wehrheim, Counterexamples in scale calculus, arxiv:1807.02591 (July 2018), to appear in PNAS (Proceedings of the National Academy of Sciences).

4. B. Filippenko, Polyfold regularization of constrained moduli spaces, arxiv:1807.00386 (July 2018).



Videos of talks

1. "Fiber products of polyfolds and the PSS morphism" (video), Workshop on Symplectic Field Theory IX: Polyfolds for SFT (conference website), University of Augsburg, August 2018.

2. "Local models of M-polyfolds, strong bundles, sc-Fredholm sections" (video), precourse to the Workshop on Symplectic Field Theory IX: Polyfolds for SFT (conference website), University of Augsburg, August 2018.