My research interests are in geometry, topology, and their applications. In particular, I am focused on inverse problems for topological and geometric invariants, topological optimization and approximation, learning with topological invariants, and the connections between them. I have also been working in the area of data fusion, using techniques from geometry and topology to analyze and synthesize time series data.

## Publications & Preprints

**A Convolutional Persistence Transform**(with Paul Bendich)

[arXiv]

We combine convolutions and persistent homology to develop a new injective topological transform. We demonstrate experimentally that this pipeline greatly increases the power of topological features, even using random filters and vectorizing diagrams using only total persistence.

**Improving Metric Dimensionality Reduction with Distributed Topology**

(with Alex Wagner and Paul Bendich)

[arXiv]

We use distributed persistence and local geometry to define a new dimensionality-reduction pipeline, **DIPOLE**.

**From Geometry to Topology: Inverse Theorems for Distributed Persistence** (with Alex Wagner and Paul Bendich) [SoCG]

We propose a distributed persistence invariant which provably interpolates between geometry and topology.**Here is a recording of a talk I gave about this paper at ATiA.**

**A Fast and Robust Method for Global Topological Functional Optimization** (with Alex Wagner and Paul Bendich) [AISTATS]

We propose a new framework for optimizing topological functionals on simplicial complexes that is faster, and produces more robust optima, than prior methods.

**Geometric Fusion via Joint Delay Embeddings **(with Paul Bendich) [Fusion2020]

We use geometric and topological methods to fuse time series. *Won 2nd runner up in the general category of the Fusion 2020 Best Paper Award!*

**Intrinsic Topological Transforms via the Distance Kernel Embedding (with Clément Maria, Steve Oudot)**

[SOCG]

We use spectral geomety to define a novel topological transform.

**Inverse Problems in Topological Persistence**** (with Steve Oudot)**

[Proceedings of the Abel Symposium]

A survey of inverse problems in applied topology.

**Barcode Embeddings for Metric Graphs (with Steve Oudot) **

[Algebraic and Geometric Topology]

We study the inverse problem for the intrinsic persistent homology transform on metric graphs.

**Relaxing the Integral Text: A Challenge for the Advanced ****Calculus Student (with Paul Carter)**

[College Mathematics Journal]