Luis Scoccola

Mathematician and computer scientist working in computational topology and geometry, and applications to machine learning and data science.

Math+CS (U. Buenos Aires), PhD math (Western U.), postdoc math (Michigan State U. → Northeastern U. → U. of Oxford)

Publications, Preprints, and Software

[google scholar]

Persistence 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

w/ Magnus B. Botnan, Steffen Oppermann, Steve Oudot [arXiv] (2022)
On the stability of multigraded Betti numbers and Hilbert functions

SIAM Journal on Applied Algebra and Geometry (2023, to appear) [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

Proc. 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

Proc. 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

w/ Alexander Rolle [arXiv] (2023)
Stable vectorization of multiparameter persistent homology using signed barcodes as measures

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

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

Dimensionality reduction based on topological persistence
Journal of Open Source Software (2023) [github] [pypi] [docs]
w/ Jose A. Perea and Chris Tralie

Univalent Foundations and Homotopy Type Theory

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

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