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?

My favourite open problem is the Aldous-Lyons conjecture, which generalizes to graphings the Sofic problem for groups.

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

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]