Hi there! I am Anibal Maximiliano 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 at Stony Brook, I worked for Stanford, Notre Dame, EPFL, MPIM, and Paris Nord.
Contact
anibal.medina.mardones (“at”) uwo.ca
Preprints
- With F. Cantero-Morán. Connected power operations and simplicial Poincaré duality
- With F. Cantero-Morán. An effective proof of the Cartan formula: Odd primes.
- With M. Rivera. Adams’ cobar construction as a monoidal E∞-coalgebra model of the based loop space.
- An axiomatic characterization of Steenrod’s cup-i products.
- With G. Friedman and D. Sinha. Foundations of geometric cohomology: from co-orientations to product structures.
Publications
- With G. Friedman and D. Sinha. Flowing from intersection product to cup product. J. Topol. Anal. (To appear)
- With A. Pizzi and P. Salvatore. Multisimplicial chains and configuration spaces. J. Homotopy Relat. Struct. (To appear)
- Ranicki-Weiss assembly and the Steenrod constructions. Proc. Amer. Math. Soc. 2024.
- With U. Bauer and M. Schmahl. Persistent homology for functionals. Commun. Contemp. Math. 2023.
- The diagonal of cellular spaces and effective algebro-homotopical constructions. EMS Surv. Math. Sci. 2023.
- New formulas for cup-i products and fast computation of Steenrod squares. Comput. Geom. 2023.
- With R. Kaufmann. A combinatorial E∞-algebra structure on cubical cochains and the Cartan-Serre map. Cahiers Topologie Géom. Différentielle Catég. 2022.
- With U. Lupo and G. Tauzin. Persistence Steenrod modules. J. Appl. Comput. Topol. 2022.
- A finitely presented E∞-prop II: cellular context. High. Struct., 2021.
- A computer algebra system for the study of commutativity up to coherent homotopies. Tbilisi Math. J., 2021.
- With R. Kaufmann. Cochain level May-Steenrod operations. Forum Math., 2021.
- With G. Brumfiel and J. Morgan. A cochain level proof of Adem relations in the mod 2 Steenrod algebra. J. Homotopy Relat. Struct., 2021.
- With F. Rosas, S. Rodríguez and R. Cofré. Hyperharmonic analysis for the study of high-order information-theoretic signals. Journal of Physics: Complexity, 2021.
- 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.
- An algebraic representation of globular sets. Homology Homotopy Appl., 2020.
- An effective proof of the Cartan formula: the even prime. J. Pure Appl. Algebra, 2020.
- 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
- ComCH: A computer algebra system for the study of commutativity up to coherent homotopies. GitHub – Docs
- With U. Lupo & G. Tauzin. steenroder: Higher-order self-intersections in persistence homology. GitHub
- With G. Tauzin et. al. giotto-tda: A high performance topological machine learning toolbox. GitHub – Docs
- simplicial_operators: A package to define and manipulate the algebra of simplicial operators. GitHub
- wcat: pasting diagrams and free omega-categories. GitHub
Selected Jupyter Notebooks
- The Barratt-Eccles operad (2020) Binder
- The surjection operad (2020) Binder
- Chain level Steenrod operations (2020) Binder
- An effective construction of Cartan coboundaries (2019) Colab or Binder
- The algebra of simplicial operators (2019) Colab – Binder
- The Alexander-Whitney, Eilenberg-Zilber, and Shih maps (2019) Colab – Binder
- An E∞-structure via the diagonal and join maps (2019) Colab – Binder
- E∞-bialgebra structure on chains of standard cubes (2019) Colab
- Steenrod squares and cup-i products (2018) Colab – Binder
Profile at GitHub