Álvaro Ribot

PhD Student at Harvard University
aribotbarrado [at] g.harvard.edu

About

Hi! I'm a third-year PhD Student in Applied Mathematics at Harvard University, where I am fortunate to be advised by Anna Seigal. My research is being supported by "la Caixa" Foundation and Real Colegio Complutense fellowships.

Before joining Harvard, I graduated in Mathematics and Data Science at the Polytechnic University of Catalonia (UPC), supported by a CFIS scholarship. I pursued my bachelor's thesis at MIT advised by Caroline Uhler.

Research

My research interests lie in the nexus between applied algebra, algebraic statistics, and machine learning theory. I am broadly interested in using algebraic tools to study problems in data science. My research is currently focused on tensor decomposition and graphical models.

Articles:

Beyond independent component analysis: identifiability and algorithms
with Anna Seigal and Piotr Zwiernik
Preprint
Orthogonal eigenvectors and singular vectors of tensors
with Anna Seigal and Piotr Zwiernik
Preprint
Halfspace Representations of Path Polytopes of Trees
with Amer Goel and Aida Maraj
Preprint
Toric Multivariate Gaussian Models from Symmetries in a Tree
with Emma Cardwell and Aida Maraj
Advances in Applied Mathematics 174, 103024 (2026) [pdf] [arXiv] [code]
Decomposing tensors via rank-one approximations
with Emil Horobet, Anna Seigal, and Ettore Teixeira Turatti
SIAM Journal on Matrix Analysis and Applications 47, 282-307 (2026) [pdf] [arXiv]
Causal Imputation for Counterfactual SCMs: Bridging Graphs and Latent Factor Models
with Chandler Squires and Caroline Uhler
3rd conference on Causal Learning and Reasoning, PMLR 236, 1141-1175 (2024) [pdf] [arXiv] [code]

Conferences

  • Recent Developments on Lattice Polytopes in Leipzig, MPI MIS, Leipzig, Germany, January 2026
  • New Directions in Algebraic Statistics, IMSI, Chicago, IL, July 2025.
  • SIAM Conference on Applied Algebraic Geometry, University of Wisconsin-Madison, July 2025.
  • Summer School in Total Positivity and Quantum Field Theory, Harvard CMSA, June 2025.
  • Joint Mathematics Meetings, Seattle, WA, January 2025.
  • Workshop on Current Methods and Open Problems in Mathematical and Statistical Phylogenetics, ICERM, Providence, RI, September 2024.
  • Effective Methods in Algebraic Geometry (MEGA), MPI MiS, Leipzig, Germany, July 2024.
  • AlToGeLiS, MPI CBG, Dresden, Germany, May 2024.
  • Causal Learning and Reasoning, UCLA, April 2024.
  • Mathematics in Science: Perspectives and Prospects, Harvard University, October 2023.
  • Hypatia Graduate Summer School, CRM, Barcelona, Spain, June 2023.
  • JAE School of Mathematics, ICMAT, Madrid, Spain, June 2021.

Activities

January 2026: I visited Bernd Sturmfels at the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany.
July 2025: I organized, with Kexin Wang, a minisymposium at the SIAM Conference on Applied Algebraic Geometry called "Algebraic Structure in Numerical Computations".
Spring 2025: I organized, with Emma Cardwell and Kexin Wang, a reading group on Numerical Algebraic Geometry.
Summer 2024: I organized, with Aida Maraj, an REU (Research Experience for Undergraduates) on Algebraic Geometry of Multivariate Gaussian Models.

Teaching

Algebraic Fundamentals of Representing Data (Applied Math 210)
Harvard University, Fall 2025, Guest Lecturer [website]
Algebra for Models and Data (Applied Math 106)
Harvard University, Spring 2025, Teaching Assistant [website]
Seminar on Fourier Analysis
CFIS-UPC, Spring 2022, Course Instructor [syllabus (in Catalan)]
First-year courses: Algebra, Calculus, Geometry, Discrete Mathematics
CFIS-UPC, AY 2021-22, Teaching Assistant