Luis Scoccola

Mathematician and computer scientist working in computational topology & geometry, representation theory, and machine learning. From foundations to software.

Math+CS@U. Buenos Aires, PhD Math@U. Western Ontario,
Postdoc Math@Michigan State U.→Northeastern U.,
Postdoc Math@U. Oxford,
CRM-ISM postdoc fellow@LaCIM/UQÀM+U. Sherbrooke

Articles and Software

Persistence Theory and Representation Theory of Posets

Generic multi-parameter persistence modules are nearly indecomposable

w/ Ulrich Bauer [arXiv] (2023)
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
Rectification of interleavings and a persistent Whitehead theorem

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

PhD dissertation (2020)

Computational Topology and Geometry

Approximate and discrete Euclidean vector bundles

Forum of Mathematics, Sigma (2023) [arXiv]
L.S., Jose A. Perea
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

Machine Learning with Topology and Geometry

Stable and consistent density-based clustering via multiparameter persistence

Journal of Machine Learning Research (to appear, 2024) [arXiv]
w/ Alexander Rolle
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 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

Type Theory and Univalent Foundations

The Hurewicz theorem in homotopy type theory

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

Software

Persistable: persistent and stable clustering

Clustering based on multiparameter persistence, with extensive visualization features.
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