Alvaro Ribot

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

About

I am a fourth-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

I am broadly interested in applying tools from algebra and geometry to solve problems in statistics and data science. My research lies in applied algebra, tensor decomposition, algebraic statistics, and machine learning theory.

Articles:

Unifying singular value decompositions of tensors via aligned orthogonality
Preprint
Causal discovery under mean independence and linearity
with Geert Mesters, Anna Seigal, and Piotr Zwiernik
Preprint [code]
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) [journal] [code]
Decomposing tensors via rank-one approximations
with Emil Horobet, Anna Seigal, and Ettore Turatti
SIAM Journal on Matrix Analysis and Applications 47, 282-307 (2026) [journal]
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) [journal] [code]

Activities

2027

Spring: Attending the semester program Metric Algebraic Geometry: Going Global at ICERM (Providence, Rhode Island, US).
January 12 - 15: Attending JMM 2026 (Chicago, Illinois, US).

2026

December 11 - 14: Attending CMS Winter Meeting (Montreal, Canada).
November 16 - 20: Attending SIAM MDS26 and giving a talk at the Geometric and Algebraic Foundations of Deep Learning minisymposium (Salt Lake City, Utah, US).
Fall: Organizing a reading group in nonlinear algebra at Harvard (Cambridge, Massachusetts, US).
August 31 - September 4: Giving a talk at INABAG 2026 (Siena, Italy).
July 25 - 26: Attending Y Combinator's Startup School (San Francisco, California, US).
July 20 - 23: Attending ICMS 2026 and giving a talk at the session on Biological Applications of Computer Algebra (Waterloo, Ontario, Canada).
July 6 - 10: Attending SIAM AN26 and giving a talk at the Algebraic Statistics minisymposium (Cleveland, Ohio, US).
June 22 - 26: Giving a lightning talk at the conference on Metric Algebraic Geometry at Institut Mittag-Leffler (Stockholm, Sweden).
May 28 - June 3: Visiting Yulia Alexandr at UCLA and giving a talk at the Math Machine Learning Group seminar (Los Angeles, California, US).
April 29: Giving a talk at BARÇAS: Barcelona Algebraic Statistics seminar at UPC (Barcelona, Spain).
April 28: Giving a talk at the Managerial Decision Sciences seminar at IESE Business School (Barcelona, Spain).
February 13: Giving a talk at the Harvard Applied Math and Statistics Lightning Talks (Cambridge, Massachusetts, US).
January 29: Giving a talk at the Math Seminar at CSBD (Dresden, Germany).
January 7 - February 4: Visiting Bernd Sturmfels at the Max Planck Institute for Mathematics in the Sciences and giving a talk at the Nonlinear Algebra Group seminar (Leipzig, Germany).

2025

July 21 - 25: Giving a talk at the conference on New Directions in Algebraic Statistics at IMSI (Chicago, Illinois, US).
July 7 - 11: Attending SIAM AG25, organizing the Algebraic Structure in Numerical Computations minisymposium with Ada Wang, and giving a talk at the Applications of Algebraic Geometry to the Ranks of Tensors minisymposium (Madison, Wisconsin, US).
June 2 - 4: Attending the summer school on Total Positivity and Quantum Field Theory at Harvard CMSA (Cambridge, Massachusetts, US).
Spring: Organizing with Emma Cardwell and Ada Wang a reading group on Numerical Algebraic Geometry at Harvard University (Cambridge, Massachusetts, US).
February 6: Giving a talk at the Math Machine Learning seminar MPI MIS + UCLA (online).
January 8 - 11: Attending JMM 2025 and giving a talk at the session on Algebraic Methods in Machine Learning and Optimization (Seattle, Washington, US).

2024

September 20: Attending the workshop on Current Methods and Open Problems in Mathematical and Statistical Phylogenetics at ICERM (Providence, Rhode Island, US).
July 29 - August 2: Presenting a poster at MEGA 2024 (Leipzig, Germany).
Summer: Organizing with Aida Maraj a Research Experience for Undergraduates on Algebraic Geometry of Multivariate Gaussian Models at Harvard University (Cambridge, Massachusetts, US).
May 3 - 4: Attending AlToGeLis 2024 at MPI-CBG (Dresden, Germany).
April 1 - 3: Presenting a poster at CLeaR 2024 (Los Angeles, California, US).

2023

June 5 - 8: Attending Hypatia Graduate Summer School at CRM (Barcelona, Spain).

Teaching

Algorithms for Data Science (Computer Science 2243)
Teaching Fellow with Prof. Sitan Chen
Harvard University, Fall 2026 [website]
Algebraic Fundamentals of Representing Data (Applied Math 210)
Guest Lecturer
Harvard University, Fall 2025 [website]
Algebra for Models and Data (Applied Math 106)
Teaching Fellow with Prof. Anna Seigal
Harvard University, Spring 2025 [website]
Fourier Analysis Seminar
Course Instructor
CFIS-UPC, Spring 2022 [syllabus (in Catalan)]
Mathematical Problem Solving Workshop
Course Instructor
CFIS-UPC, Fall 2021 - Spring 2022