Luis Scoccola

w/ Ulrich Bauer, Thomas Brüstle [arXiv]

w/ Ulrich Bauer, Cameron Gusel [arXiv]

w/ Thomas Brüstle, Steve Oudot, Hugh Thomas [arXiv]

w/ Benjamin Blanchette, Justin Desrochers, Eric J Hanson [arXiv]

w/ Riju Bindua, Thomas Brüstle [arXiv]

International Mathematics Research Notices (2025) [arXiv]
w/ Ulrich Bauer

Symp. on Computational Geometry (SoCG 2025) (conference version)
[arXiv] (journal version)
w/ Yuan Luo, Dmitriy Morozov

Advances in Mathematics (2024) [arXiv]
w/ Magnus B. Botnan, Steffen Oppermann, Steve Oudot

SIAM Journal on Applied Algebra and Geometry (2024) [arXiv]
w/ Steve Oudot

Forum of Mathematics, Sigma (2023) [arXiv]
w/ Jose A. Perea

Algebraic & Geometric Topology (2023) [arXiv]
w/ Edoardo Lanari

Algebraic & Geometric Topology (2023) [arXiv]
w/ Dan Christensen

PhD dissertation, University of Western Ontario (2020)

Mathematical Structures in Computer Science (2020) [arXiv]

Higher Structures (2020) [arXiv]
w/ Dan Christensen, Morgan Opie, Egbert Rijke

Symp. on Logic in Computer Science (LICS 2020) [arXiv]
w/ Thorsten Altenkirch

International Conference on Machine Learning (ICML 2025) [arXiv]
L.S., Uzu Lim, Heather A. Harrington

International Conference on Machine Learning (ICML 2024) [arXiv]
{L.S., Siddharth Setlur}, David Loiseaux, Mathieu Carrière, Steve Oudot

Journal of Machine Learning Research (2024) [arXiv]
{Alexander Rolle, L.S.}

Neural Information Processing Systems (NeurIPS 2023) [arXiv]
{David Loiseaux, L.S.}, Mathieu Carrière, Magnus B. Botnan, Steve Oudot

Symp. on Computational Geometry (SoCG 2023) [arXiv]
L.S., Hitesh Gakhar, Johnathan Bush, Nikolas Schonsheck, Tatum Rask, Ling Zhou, Jose A. Perea

Symp. on Computational Geometry (SoCG 2023) [arXiv]
L.S., Jose A. Perea

Learn covers of data using geometric optimization, for topological inference and visualization. [github]
L.S., Uzu Lim

High performance implementation using Numba, intended for clustering. [github] [pypi] [docs]

Density-based clustering for exploratory data analysis based on multi-parameter persistence.
Journal of Open Source Software (2023) [github] [pypi] [docs]
L.S., Alexander Rolle

Topology-based dimensionality reduction.
Journal of Open Source Software (2023) [github] [pypi] [docs]
w/ Jose A. Perea, Chris Tralie

Artificial Intelligence can be applied to many math-related tasks, including formal and informal theorem proving, formalization and informalization, and math discovery. In order to make long term progress, it is necessary to have a good understanding of each task, of their relationships, and of what is currently within reach.

Proof assistants enable us to formalize mathematics: to express arbitrary mathematical statements and proofs without ambiguity, and to automatically verify their correctness. Here I give some arguments for why math formalization might soon become inevitable. I also include some resources on formalization for the interested reader.

The standard approach to Topological Inference is based on geometric complexes. Most commonly, geometric complexes scale cubically (and often worse) in the number of data points, which poses a big problem. Here I describe an alternative approach to Topological Inference.

Fundamental problems in classical Unsupervised Learning, such as Clustering and Dimensionality Reduction, can be fruitfully interpreted from the point of view of Topological Inference. This is an introduction to this point of view.