• Nathaniel Gorski, Xin Liang, Hanqi Guo, Lin Yan, and Bei Wang. A general framework for augmenting lossy compressors with topological guarantees. IEEE TVCG journal track at IEEE PacificVis 2025.

Topology-Preserving Compression of 2D Tensor Fields

• Designed a framework that augments any error-bounded lossy compressor to preserve topological features of 2D symmetric and asymmetric tensor fields while maintaining a user-specified error bound

• Wrote custom scientific visualizations for tensor fields

Extracting the Topology of Loss Landscapes

•  Currently studying how the topology of the loss function of a deep neural network interacts with training

• Visualized the loss function of deep neural networks on 2D linear subspaces of the parameter space

Contour Tree Preserving Data Compression

• Designed a framework that augments any lossy compressor to preserve the contour tree of scalar field data which is applicable to both classic and deep learning data compressors

• Compared to the state-of-the-art, improved compression ratios by 2.8-6.8x and reduced running times by 25-95% while maintaining similar reconstruction quality

In order to receive my BS with honors, I wrote a thesis on differential topology. It is a summary of an independent study that I completed on differential topology. None of the material was copied verbatum, and many of the proofs are completely original.

My undergraduate thesis was titled "Oriented Intersection in Differential Topology". My thesis advisor was Craig Westerland. You can read it here.

To receive my M.A.T., I wrote an extended literature review about perfectionism among adolescents. The title of the paper is "The Causes and Effects of Perfectionism Among High School Students." My advisor is Il-Hee Kim. You can read it here.

I did research in algebraic combinatorics during Spring 2018 with one of my graduate TAs. The problem that I sought to solve was to find the largest subset of a cyclic group of order n such that no k elements of the subset summed up to 0, for any given n and k. I solved the problem in the case where n and k meet certain conditions.

This research was inspired by the work of Bela Bajnok. I worked under Ryan Matzke, a former student of Bajnok.

I presented the results of my research at the CeSMR Conference at the University of Nebraska - Lincoln.

You can find the writeup of my research here. These notes were written to summarize what I had done, so this does not represent my best technical writing. For a better example, see my undergraduate thesis below.