Luis Scoccola

Mathematics (15)

A metrically complete and Krull-Schmidt space of multiparameter persistence modules

w/ Ulrich Bauer, Cameron Gusel [arXiv]
Counts and end-curves in two-parameter persistence

w/ Thomas Brüstle, Steve Oudot, Hugh Thomas [arXiv]
Stabilization of the spread-global dimension

w/ Benjamin Blanchette, Justin Desrochers, Eric J Hanson [arXiv]
Decomposing zero-dimensional persistent homology over rooted tree quivers

w/ Riju Bindua, Thomas Brüstle [arXiv]
Multi-parameter persistence modules are generically indecomposable

International Mathematics Research Notices (2025) [arXiv]
w/ Ulrich Bauer
Computing Betti tables and minimal presentations of zero-dimensional persistent homology

Symp. on Computational Geometry (SoCG 2025) [arXiv]
w/ Dmitriy Morozov
On the bottleneck stability of rank decompositions of multi-parameter persistence modules

Advances in Mathematics (2024) [arXiv]
w/ Magnus B. Botnan, Steffen Oppermann, Steve Oudot
On the stability of multigraded Betti numbers and Hilbert functions

SIAM Journal on Applied Algebra and Geometry (2024) [arXiv]
w/ Steve Oudot
Approximate and discrete Euclidean vector bundles

Forum of Mathematics, Sigma (2023) [arXiv]
w/ Jose A. Perea
Rectification of interleavings and a persistent Whitehead theorem

Algebraic & Geometric Topology (2023) [arXiv]
w/ Edoardo Lanari
The Hurewicz theorem in homotopy type theory

Algebraic & Geometric Topology (2023) [arXiv]
w/ Dan Christensen
Locally persistent categories and metric properties of interleaving distances

PhD dissertation, University of Western Ontario (2020)
Nilpotent types and fracture squares in homotopy type theory

Mathematical Structures in Computer Science (2020) [arXiv]
Localization in homotopy type theory

Higher Structures (2020) [arXiv]
w/ Dan Christensen, Morgan Opie, Egbert Rijke
The integers as a higher inductive type

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

Machine Learning and Data Science (6)

Cover learning for large-scale topology representation

International Conference on Machine Learning (ICML 2025) [arXiv]
L.S., Uzu Lim, Heather A. Harrington
Differentiability and optimization of multiparameter persistent homology

International Conference on Machine Learning (ICML 2024) [arXiv]
{L.S., Siddharth Setlur}, David Loiseaux, Mathieu Carrière, Steve Oudot
Stable and consistent density-based clustering via multiparameter persistence

Journal of Machine Learning Research (2024) [arXiv]
{Alexander Rolle, L.S.}
Stable vectorization of multiparameter persistent homology using signed barcodes as measures

Neural Information Processing Systems (NeurIPS 2023) [arXiv]
{David Loiseaux, L.S.}, Mathieu Carrière, Magnus B. Botnan, Steve Oudot
Toroidal coordinates: decorrelating circular coordinates with lattice reduction

Symp. on Computational Geometry (SoCG 2023) [arXiv]
L.S., Hitesh Gakhar, Johnathan Bush, Nikolas Schonsheck, Tatum Rask, Ling Zhou, Jose A. Perea
Fiberwise dimensionality reduction of topologically complex data with vector bundles

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

Software (4)

ShapeDiscover: cover learning with geometric optimization
Learn covers of data using geometric optimization, for topological inference and visualization [github]
L.S., Uzu Lim
FufPy: fast union-find in Python
High performance implementation using Numba, intended for clustering [github] [pypi] [docs]
Persistable: clustering with multi-parameter persistence

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
DREiMac: dimensionality reduction with Eilenberg-MacLane coordinates

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

Blog (4)

Artificial Mathematical Intelligence in 2025

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.
Why math should be formalized - and resources to get started

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.
Cover Learning for Topological Inference

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.
Topological Inference and Unsupervised Learning

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.

Luis Scoccola

Papers • Software • Blog

Contact and other info

Some cool figures from my research