Anibal M. Medina-Mardones

Hi there! I am Anibal M. Medina-Mardones, a mathematician working on theoretical and applied topology. I am originally from Patagonia, Chile and the picture above shows Cerro Castillo near my hometown, Coyhaique.

I recently moved to Canada to work for Western University. Previously, after studying with Dennis Sullivan, I worked for Stanford, Notre Dame, EPFL, MPIM, and Paris Nord.

Contact

  anibal.medina.mardones (“at”) uwo.ca

Students

Excited about topology and interdisciplinary research? I’m looking for MSc and PhD students to join our fully funded programs. Interested? Find out more about the application process here.

Preprints

  1. With L. Zhou. Persistent cohomology operations and Gromov-Hausdorff estimates.
  2. With Shehper et al. What makes math problems hard for reinforcement learning: a case study.
  3. With F. Cantero-Morán. Connected power operations and simplicial Poincaré duality.
  4. An axiomatic characterization of Steenrod’s cup-i products.
  5. With G. Friedman and D. Sinha. Foundations of geometric cohomology: from co-orientations to product structures.

Publications

  1. With F. Cantero-Morán. An effective proof of the Cartan formula: Odd primes. Homology Homotopy Appl. (To appear)
  2. With G. Friedman and D. Sinha. Flowing from intersection product to cup product. J. Topol. Anal. 2024
  3. With M. Rivera. Adams’ cobar construction as a monoidal E∞-coalgebra model of the based loop space. Forum Math. Sigma. 2024
  4. With A. Pizzi and P. Salvatore. Multisimplicial chains and configuration spaces. J. Homotopy Relat. Struct. 2024
  5. Ranicki-Weiss assembly and the Steenrod constructions. Proc. Amer. Math. Soc. 2024.
  6. With U. Bauer and M. Schmahl. Persistent homology for functionals. Commun. Contemp. Math. 2023.
  7. The diagonal of cellular spaces and effective algebro-homotopical constructions. EMS Surv. Math. Sci. 2023.
  8. New formulas for cup-i products and fast computation of Steenrod squares. Comput. Geom. 2023.
  9. With R. Kaufmann. A combinatorial E∞-algebra structure on cubical cochains and the Cartan-Serre map. Cahiers Topologie Géom. Différentielle Catég. 2022.
  10. With U. Lupo and G. Tauzin. Persistence Steenrod modules. J. Appl. Comput. Topol. 2022.
  11. A finitely presented E∞-prop II: cellular context. High. Struct., 2021.
  12. A computer algebra system for the study of commutativity up to coherent homotopies. Tbilisi Math. J., 2021.
  13. With R. Kaufmann. Cochain level May-Steenrod operations. Forum Math., 2021.
  14. With G. Brumfiel and J. Morgan. A cochain level proof of Adem relations in the mod 2 Steenrod algebra. J. Homotopy Relat. Struct., 2021.
  15. With F. Rosas, S. Rodríguez and R. Cofré. Hyperharmonic analysis for the study of high-order information-theoretic signals. Journal of Physics: Complexity, 2021.
  16. With Tauzin et. al. Giotto-tda: a topological data analysis toolkit for machine learning and data exploration. J. Mach. Learn. Res., 2021. Reprinted in NeuRips 2021.
  17. An algebraic representation of globular sets. Homology Homotopy Appl., 2020.
  18. An effective proof of the Cartan formula: the even prime. J. Pure Appl. Algebra, 2020.
  19. A finitely presented E∞-prop I: algebraic context. High. Struct., 2020.

Profile at Google Scholar

Editorial

  Managing Editor. Advanced Studies: Euro-Tbilisi Mathematical Journal.

Software

Packages
  1. ComCH: A computer algebra system for the study of commutativity up to coherent homotopies. GitHub – Docs
  2. With U. Lupo & G. Tauzin. steenroder: Higher-order self-intersections in persistence homology. GitHub
  3. With G. Tauzin et. al. giotto-tda: A high performance topological machine learning toolbox. GitHub – Docs
  4. simplicial_operators: A package to define and manipulate the algebra of simplicial operators. GitHub
  5. wcat: pasting diagrams and free omega-categories. GitHub
Selected Jupyter Notebooks
  1. The Barratt-Eccles operad Binder
  2. The surjection operad Binder
  3. Chain level Steenrod operations Binder
  4. An effective construction of Cartan coboundaries Colab or Binder
  5. The algebra of simplicial operators Colab – Binder
  6. The Alexander-Whitney, Eilenberg-Zilber, and Shih maps Colab – Binder
  7. An E∞-structure via the diagonal and join maps Colab – Binder
  8. E∞-bialgebra structure on chains of standard cubes Colab
  9. Steenrod squares and cup-i products Colab – Binder

Profile at GitHub