Luis Scoccola

Luis Scoccola

About me

I am a postdoc at the Math department at Michigan State University, working with Jose Perea.

I studied Math and Computer Science at the University of Buenos Aires, and got my PhD from the University of Western Ontario, under the supervision of Dan Christensen.

Research interests

Computational Topology, its connections to Homotopy Theory, Category Theory, Metric Geometry, and Statistics, and its applications to Machine Learning and Data Analysis. I have also worked on Formalization and Homotopy Type Theory.

Publications and preprints [Google scholar]

8.  Approximate and discrete Euclidean vector bundles.
With J. A. Perea. [arXiv]

7.  Rectification of interleavings and a persistent Whitehead theorem.
With E. Lanari. [arXiv]

6.  Stable and consistent density-based clustering.
With A. Rolle. [arXiv]

5.  Locally persistent categories and metric properties of interleaving distances.
PhD dissertation. [thesis]

4.  The Hurewicz Theorem in Homotopy Type Theory.
With D. Christensen. [arXiv]

3.  Nilpotent Types and Fracture Squares in Homotopy Type Theory.
Mathematical Structures in Computer Science, 30(5):511–544, 2020. [MSCS]

2.  Localization in Homotopy Type Theory.
With D. Christensen, M. Opie, and E. Rijke.
Higher Structures, 4(1):1–32, 2020. [HS]

1.  The Integers as a Higher Inductive Type.
With T. Altenkirch.
Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science (pp. 67–73), 2020. [LICS]


4.  gamma-linkage clustering algorithm.
With A. Rolle.
From "Stable and consistent density-based clustering", above. [Git]

3.  Approximate and discrete Euclidean vector bundles.
Computational examples of the homonymous article, above. [Git]

2.  The Integers as a Higher Inductive Type.
Formalization of the homonymous article, above. [Git]

1.  A visualization tool for parameter selection in cluster analysis.
With A. Rolle. [Git]

Selected talks

July 21st, 2021 Density-based clustering and multiparameter persistence [slides], Metrics in Multiparameter Persistence workshop, Lorentz Center.
April 16th - April 28th - May 3rd, 2021 Approximate and discrete vector bundles in theory and applications [recording], Applied Topology in Albany seminar - IMSI TDA workshop - TDA, Theory and Applications TUTTE Institute and Western University
January 16th, 2021 Locally persistent categories and metric properties of interleaving distances [slides] [recording], ATMCS hosted by AATRN.
December 5th, 2020 Homotopy coherence in applied topology [slides] [recording], Canadian Mathematical Society Winter Meeting.
November 4th, 2020 Locally persistent categories and approximate homotopy theory [slides] [recording], New York City Category Theory Seminar.
June 18th, 2020 Universality of the Gromov–Hausdorff distance [slides][recording], Workshop on Topological Data Analysis, The Fields Institute.
January 31st, 2020 Quotient interleaving distances [slides], University of Florida Topological Data Analysis conference.
June 11th, 2019 Congruence in Univalent Type Theory [extended abstract][slides], TYPES, Oslo.
January 11th, 2018 Localization in Homotopy Type Theory [slides], AMS Special Session on Homotopy Type Theory, Joint Mathematics Meetings, San Diego.

Recent teaching

Spring 2021 Instructor for Calculus II, MTH 133 at MSU. If you are a student for this course, please go to the course website.
Fall 2019 Instructor for Calculus I, Math 1000 at UWO.


Summer 2020 I was awarded the Robert and Ruth Lumsden Scholarship In Science at UWO.
Spring 2020 I mentored a Directed Reading Project for an undergraduate student at UWO, on Deep Learning.
Fall 2019 I mentored a Directed Reading Project for an undergraduate student at UWO, on Category Theory.
Summer 2019MITACS grant to visit the University of Nottingham and collaborate with Thorsten Altenkirch.
May 7-11, 2018 Mathematics Research Communities collaboration grant to visit Carnegie Mellon University and collaborate with Egbert Rijke.
December 11-15, 2017 I contributed to the development of coinductive types in UniMath library, during the UniMath School, 2017.
Fall 2017 to Spring 2019 I co-organized the math graduate seminar at UWO.
March to October 2014I co-organized the seminar on functional programming at the Universidad de Buenos Aires.

Contact information, for x = scoccola

Pronoun: he