Heitor Baldo

Heitor Baldo

PhD in Bioinformatics (Mathematical Neuroscience)

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About me

Hi! My name is Heitor Baldo and I hold a BS in Mathematics and an MS in Applied and Computational Mathematics both from the University of Campinas, and a PhD in Bioinformatics (Mathematical Neuroscience) from the University of São Paulo. I was a visiting postdoctoral researcher at Leipzig University, Germany, and I’m currently a postdoctoral fellow at the University of São Paulo. I have experience in the areas of mathematics, applied mathematics, computer science, and bioinformatics, with an emphasis on mathematical neuroscience. More specifically, I am interested in the mathematical foundations of methods coming from various areas of pure and applied mathematics, such as abstract algebra, combinatorics, algebraic topology and geometry, discrete geometry, graph theory, category theory, complex systems, and complexity science, and how these methods, together with probabilistic, statistical, and computational methods, can be useful in mathematical neuroscience and mathematical biology.

Update
  • A preliminary draft of my newest manuscript is now available here.
  • A preliminary draft of my book "Topologica Algébrica Computacional: Uma Introdução" (in Portuguese) is now available here.

Research Interests

Mathematical Theories

  • Computational algebraic topology and geometry;
  • Discrete and combinatorial geometry (discrete (higher-order) structures; discrete curvatures; finite geometries);
  • Graph theory (quantitative (hyper)graph theory and network statistics; spectral (hyper)graph theory; (hyper)graph products; multilayer (hyper)graphs);
  • Matroid theory (oriented matroids; (hyper)graphic matroids; tropical matroids);
  • Category theory (categorification; monoidal categories; operads);
  • Complexity science / complex systems (complexity measures; quantitative emergence; graph celullar automata; agent-based modeling);

Applications

  • Topological data analysis of metabolic hypergraphs;
  • Multi-omics analysis through spectral properties of multilayer hypergraphs;
  • Quantitative analysis of multilayer and dynamic brain (hyper)graphs;
  • Graph theoretical analysis and topological data analysis for neuroscience (brain connectivity networks) / connectomics and neurogenetics;
  • Neural rings and combinatorial neural codes;
  • Neural manifolds and Stiefel manifolds for neural data analysis;
  • Topological/geometric deep learning.

MS and PhD Thesis

Other Information