Research

My research lies in the broad area of measured group theory. A common thread in my research is understanding measured-combinatorial generalizations of group properties. How can we use analysis, combinatorics, and geometry to understand infinite groups through their dynamics?

Some keywords for my interests include (but are not limited to) Borel combinatorics, Borel equivalence relations, cost, graphings, l_2-Betti numbers, property (T), soficity, treeability and unimodular random graphs. 

Pre-prints

• Unimodular random graphs with Property (T) have cost one. Joint with Łukasz Grabowski and Sam Mellick. 2025, available in [arXiv]

• Exactness and the topology of the space of invariant random equivalence relations. Joint with Sam Mellick, Antoine Poulin and Konrad Wróbel. 2025, available in [arXiv] 

• Applications of tree decompositions and accessibility to treeability of Borel graphs. 2023, available in [arXiv].

Publications

• Jardon-Sanchez, H., Laustsen, N., Taylor, M. A., Tradacete, P. & Troitsky, V., (2021). Free Banach lattices under convexity conditions. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. Volume 116. Article number 15. [doi] [pdf]

Undergraduate publications

• Arraz Almirall, A., Cobollo Gómez, C., Jardón-Sánchez, H., Martín Murillo, C., Quilis, A., Ribera Baraut, P. & Parissis, I, (2020). Maximal averaging operators: from geometry to boundedness through duality. TEMat monográficos, Volume 1. Pages 97 - 111. [pdf]

• Aguado López, J., Cano Mármol, A. I., Carballido Costas, A., García Fernández, M., Gómez Marín, F., Jardón-Sánchez, H., Ratsimanetrimanana, A. & Bru, J. B. (2020). Semigroup theory in quantum mechanics. TEMat monográficos, Volume 1. Pages 17 - 31. [pdf]

Dissertations

• MSc dissertation: "On group amenability and quasidiagonality" supervised by Stuart White at University of Oxford. [pdf]

• Mathematics bachelor's thesis (trabajo fin de grado): "Operadores positivos y el problema del subespacio invariante" (spanish) supervised by Antonio Martínez Abejón and Pedro Tradacete. [pdf]

• Physics bachelor's thesis (trabajo fin de grado): "Instantones y teorías de Yang–Mills" (spanish) supervised by Diego Rodríguez-Gómez. [pdf]