Research

Broadly, I’m interested in the intersection of statistical methods, algebra, and geometric tools. I am currently thinking a lot about random matrices, concentration inequalities and how they can be used for statistical applications in high-dimensional regimes. Current projects include:

• Recovering discrete spectra in random matrices

  Asymptotic results for random matrices break down when the dimensionality of a dataset is large. Can machine learning techniques bridge the gap?

• Degrees of freedom in matrix completion problems

  Are all entries in a matrix equally important? How do different methods affect the geometry of solutions in matrix approximations? And can we develop a notion of effective rank?

• Geometry is weird in high-dimensions. Can we find sharp, useful bounds for tail probabilites in such regimes?

• Open to collaborations

  If you’d like to collaborate or just talk about research, don't hesitate to reach out!

1. Tensors en estadística algebraica (Butlletí De La Societat Catalana De Matemàtiques, 2025)

   L. Sierra, M. Casanellas, P. Zwiernik.

   PDF

   @article{Sierra_Casanellas_Zwiernik_2025, title={Tensors en estadística algebraica}, url={https://revistes.iec.cat/index.php/BSCM/article/view/155883}, journal={Butlletí de la Societat Catalana de Matemàtiques}, author={Sierra, Luis and Casanellas, Marta and Zwiernik, Piotr}, year={2025}, month={Oct.}, pages={131–169} }
   }

2. Tensors in Algebraic Statistics (Conference/Journal, 2024)

   M. Casanellas, L. Sierra, P. Zwiernik.

   PDF Code Talk

   @inproceedings{your2024paper,
     title={Paper Title One},
     author={Author A and Your Name and Author C},
     booktitle={Venue},
     year={2024}
   }