Research

My background is in algebraic geometry. I am interested in the both-ways connections between algebraic geometry and the fields of statistics, machine learning, and the natural sciences. I am co-advised by Bernd Sturmfels and Christiane Görgen.

Algebraic statistics investigates statistical models that are algebraic or semi-algebraic sets. It is the algebraic counterpart to information geometry. We interpret a model as a geometric object whose points correspond to its probability distributions. Then, we use tools and ideas from algebraic geometry and commutative algebra to study it.

These are the topics currently on my mind:

  1. Algebraic statistics, Mathematical statistics and mathematics of data.
  2. Graphical models, staged tree models, Bayesian networks.
  3. Maximum Likelihood Estimation problems, ML Degree.
  4. Random geometry and topology.
  5. Singular learning theory.

Papers & Preprints:

  1. covariance model, with J. I. Coons and M. Ruddy, arXiv:1909.04553 pdf
  2. Global projections of the soil microbiome, with C. Guerra,
    M. Delgado Baquerizo, E. DuarteC. Goergen, F. T. Maestre and N. Eisenhauer, submitted.
  3. Discrete statistical models with rational maximum likelihood estimator, with E. Duarte and B. Sturmfels, arXiv:1903.06110 pdf
  4. Random points on an algebraic manifold, with P. Breiding, arXiv:1810.06271 pdf
  5. Verlinde bundles of families of hypersurfaces and their jumping lines, Beitr. Algebra Geom. (2018) v2 pdf

Other writings:

  1. My definition of the chain event graph associated to a given staged tree model.
  2. My Master’s Thesis
  3. My Bachelor’s Thesis

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