Heitor Baldo

Heitor Baldo

PhD candidate in Mathematical Neuroscience

Home Page

About me

Hi! My name is Heitor Baldo and I hold a B.S. in Mathematics and a M.S. in Applied and Computational Mathematics, both from the University of Campinas. Currently, I’m a Ph.D. candidate in Bioinformatics (Mathematical Neuroscience) 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 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.

Research Interests

Mathematics and Applied Mathematics

  • Graph Theory. Quantitative graph theory. Spectral graph theory. Topological and geometric graph theory. Graph matching. Multilayer graphs. Dynamic graphs. Subgraph discovery. Hypergraphs.
  • Combinatorics and Discrete Geometry. Matroids, oriented Matroids, and tropical matroids. Finite geometries. Discrete curvatures. Polyhedral complexes.
  • Applied Algebraic Topology. Simplicial complexes. Simplicial homology. Path Homology. Persisent homology. Discrete Morse theory. Cellular sheaves. Q-Analysis.
  • Applied Algebraic Geometry. Neural rings and neural ideals. Gröbner bases. Hilbert schemes.
  • Tropical Algebra and Geometry. Tropical linear algebra. Tropical polynomials. Tropical varieties. Tropical polytopes.
  • Applied Category Theory. Categorification. Hypergraph categories. Monoidal categories and Operads.
  • Complexity Science. Complexity. Graph cellular automata. Quantitative emergence.

Artificial Intelligence

  • Machine Learning. Scientific machine learning. Topological, categorical, and geometric deep learning. Tensor networks. Recurrent neural networks. Reinforcement learning.

Mathematical Neuroscience

  • Neural Coding. Theory of combinatorial neural codes. Neural rings. Applications of oriented matroids on the theory of combinatorial neural codes. Combinatorial neural codes from the perspective of tropical algebra and geometry.
  • Network Neuroscience. Methods in brain connectivity inference (PDC, DTF). Graph theoretical analysis and topological data analysis of brain connectivity networks. Brain dynamics and Q-Analysis / directed Q-Analysis. Brain dynamics and cellular sheaves. Brain higher-order networks and hypergraphs. Network complexity of brain networks. Modeling dynamic brain networks through graph cellular automata.
  • Neural Information and Cognition. Category theory applied to the modeling of information neural networks and to the mathematical modeling of cognition.
  • Natural/Artificial Neural Computation and AI in Neural Data Analysis. Topological, categorical, and geometric deep learning techniques applied in neural data analysis. Associative memory and Hopfield networks. Interplay between AI and neuroscience.
  • Multiscale Brain Modeling. AdS/Brain correspondence (brain MERA tensor networks). Multiscale tensor networks.

Mathematical Biology

  • Biological Networks. Gene regulatory networks. Gene co-expression networks. Phylogenetics networks.

  • DNA/RNA-Related. Topological Data Analysis of RNA transcriptome. Modeling DNA and RNA mutations via graph theory and matroid theory.

Master’s Thesis and PhD Thesis

Other Information

I’m an affiliate researcher at the Institute for Globally Distributed Open Research and Education (IGDORE).