Nicholas Karris

nkarris [at] ucsd [dot] edu

Hello!

I am a fifth year Mathematics PhD student at UC San Diego. My advisor is Alex Cloninger. Starting Fall 2026, I will be a (postdoctoral) Assistant Professor at the University of Michigan.

Very broadly, my interests center around data science and machine learning. Most of my current work involves applying (linearized) optimal transport to problems involving measure-valued data, such as particle system simulations, hyperspectral imaging, and diffusion models. See Research for more detail and a list of papers.

I graduated from Northwestern University in 2021 with a BA in Mathematics and a minor in Computer Science. I wrote an honors thesis advised by Ezra Getzler.

Here is a copy of my academic CV (updated 06/2026).

Research

My research centers around the mathematics of data science and machine learning, with a recent bent towards problems involving data which is fundamentally measure-valued. In these situations, many natural questions arise about how one should perform standard data science tasks. My work answers these questions by viewing the measures themselves as single points and leveraging the tools of optimal transport and the geometry of the Wasserstein manifold to develop intuitive analogs of standard data science techniques for measure-valued data. By computing optimal transport maps from a fixed reference, we embed each measure into a common linear space (the tangent space of the Wasserstein manifold at the fixed reference), which allows us to apply out-of-the-box methods on the embeddings. When the data is static, we use these methods to build classifiers, generate new measures from particular classes, and interpolate between measures with geodesics, and when the data is evolving in time, we describe numerical methods for approximating the evolution, finding steady state distributions, and analyzing stability.

Papers

Here are the papers that I have worked on (in reverse-chronological order):

  1. H.Vandecasteele, N. Karris, A. Cloninger, I. Kevrekidis. Newton–Krylov Methods for Computing Steady States of Particle Timesteppers via Optimal Transport. Preprint, arXiv:2512.24567 [math.NA] (2025).

  2. N. Karris, L. Durell, J. Flores, T. Emerson. Which Way From B to A: The Role of Embedding Geometry in Image Interpolation for Stable Diffusion. Accepted, TAG–Data Science Conference. Preprint, arXiv:2511.12757 [cs.CV] (2025).

  3. J. Lentz, N. Karris, J. Murphy, A. Cloninger. Unbalanced Optimal Transport Dictionary Learning for Unsupervised Hyperspectral Image Clustering. Accepted, 2025 Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS) (2025). Preprint, arXiv:2603.10132 [cs.CV] (2025).

  4. N. Karris, E.A. Nikitopoulos, I. Kevrekidis, S. Lee, A. Cloninger. Using Linearized Optimal Transport to Predict the Evolution of Stochastic Particle Systems. Preprint, arXiv:2408.01857 [math.NA] (2025).

  5. J. Linwu, V. Khurana, N. Karris, A. Cloninger. Linearized Optimal Transport pyLOT Library: A Toolkit for Machine Learning on Point Clouds. Preprint, arXiv:2502.03439 [stat.ML] (2025).

Presentations

Here are the presentations I've done (in roughly reverse-chronological order):

  1. Which Way From B to A: The Role of Embedding Geometry in Image Interpolation for Stable Diffusion

  2. Using Linearized Optimal Transport to Predict the Evolution of Stochastic Particle Systems

  3. Linearized Optimal Transport on Particle Systems and Related Applications

  4. Diffusion Models and Optimal Transport

  5. Time Series on the Wasserstein Manifold

  6. Cliques, Covers, Cycles, and Salesmen: Reducing Hard Problems to Harder Ones

Teaching

Currently as a TA at UCSD:

Previously as a TA at UCSD:

As a TA at Northwestern:

Other Stuff

I am the current chair of UCSD's Mathematics Graduate Student Council (MGSC) for the academic year 25–26. I was also chair in AY 24–25, and before that, I was the Vice Chair in AY 23–24, and I served on the Mentorship Committee and Survey Committee in AY 22–23.

I have a Twitter, but I do not tweet often. I mostly use it as my source for sports news and discourse. I also have a LinkedIn, but I am even less active there. For all practical purposes, I do not have any other social media.

Okay, I think that's it! I'm not sure what else to put here. If I come up with anything, I'll add it... eventually.

Last updated: 8 Jun 2026