Members

Elba Garcia-Failde is an associate professor (maîtresse de conférences) at the Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG) of Sorbonne Université in the group "Topologie et Géométrie Algébriques". Previously, she was a postdoctoral researcher in Paris, first as a Hadamard fellow at the IPhT of Paris-Saclay and at the IHES, and then at the Université Paris Cité. She completed a PhD in the MPIM in Bonn under the guidance of G. Borot and D. Zagier. In July 2025, she will become a "Ramón y Cajal" researcher at UPC.

Garcia-Failde's interests lie at the interface between geometry and mathematical physics. More precisely, her research has four main different directions that nourish each other, as part of the rich web of ideas surrounding the topological recursion: intersection theory on the moduli space of curves, integrable systems, combinatorial and random maps (graphs embedded on surfaces), and non-perturbative extensions (mainly through resurgence). Topological recursion, initially discovered in the realm of large asymptotic expansions in random matrix theory, has evolved into a universal theory, revealing a common structure across diverse mathematical and physical domains. Taking a spectral curve as input, it recursively produces a family of multi-differentials living on the associated Riemann surface.

Her contributions include the solution of the negative analog of Witten's r-spin conjecture through a suitable deformation of a cohomological field theory, unveiling new tautological relations; large genus asymptotics of intersection numbers through a universal program, making use of resurgence techniques; a universal duality which implements moment-cumulant relations, solving an open problem in free probability and a conjecture in combinatorics of maps; the quantisation of spectral curves through topological recursion.

Søren Dyhr is a PhD student at the Universitat Politècnica de Catalunya (advisors E. Miranda with A. Gonzalez Prieto and D. Peralta-Salas), previously doing his bachelor's and master's degrees at the University of Aarhus, Denmark.

He is interested in interplays between mathematics and physics, currently in fluid dynamics. He is working on using representation theory to study embeddings of dynamical systems into fluid mechanics with possible applications to learning more about computability in this setting. 

Benedetta Facciotti is a PhD student at the University Politecnica de Catalunya working under the main supervision of Marta Mazzocco and the external cosupervision of Nikita Nikolaev. She spent the first two years of her PhD in Birmingham, and previously she obtained both her Bachelor's and Master's degree at the University of Padua, Italy.

Benedetta's interests revolve around the irregular Riemann--Hilbert correspondence. More precisely, she is looking at the different formulations of the moduli spaces of monodromy data of meromorphic differential systems, trying to understand the connection between them. By doing this, she exploits tools coming from representation theory, standard and higher Teichmuller theory and cluster algebras. 

Pablo Nicolás is a doctoral student under the supervision of Eva Miranda at Centre de Recerca Matemàtica since November 2023. Previously, he studied the bachelor's degrees in Mathematics and Physics Engineering at Universitat Politècnica de Catalunya, within the CFIS programme. Afterwards, he obtained the master's degree in Advanced Mathematics and Mathematical Engineering at Universitat Politècnica de Catalunya.

Pablo's research broadly concerns the study and classification of Poisson structures for smooth manifolds. More specifically, he is interested in the computation of invariants in Poisson geometry. In his master's thesis he computed the Poisson cohomology groups for b^m-Poisson manifolds. He is currently investigating the topology of b^m-tangent bundles and edge structures. Such objects fall within the framework of E-symplectic manifolds, which are used to study Poisson structures from the setting of singular symplectic geometry. These structures arise in problems from physics, such as in the compactification of the three-body problem and the description of twistor spaces.

Juan Brieva got his undergraduate double degree in Mathematics and Physics at CFIS with an undergraduate thesis developed in collaboration with the University of Oxford. He did his undergraduate thesis under joint supervision of Andrew Dancer (University of Oxford) and Eva Miranda (UPC). 

His undergraduate thesis entitled From symplectic geometry and group actions to singular symplectic structures deals with the study of symplectic reduction in stratified and singular symplectic manifolds.

Leonardo Costa Lesage is finishing his undergraduate double degree in Mathematics and Physics at CFIS. He is currently writing his undergraduate thesis at the University of Oxford, under joint supervision of Prof. Raymond Pierrehumbert and Prof. Eva Miranda.

His undergraduate thesis is entitled Exoplanet detection, escape orbits, and singular contact structures and deals with the singular generalized Weinstein conjecture, as well as periodic, aperiodic and escape orbits in exoplanetary systems, using the tools of singular contact geometry ($b^m$-manifolds).

Isaac Ramos Reina recently completed his undergraduate degree in Mathematics and Physics at the Universidad Complutense de Madrid. During the final year of his studies, he spent an academic year at the University of California, Los Angeles (UCLA) as an undergraduate exchange student.

He carried out his undergraduate thesis under the supervision of Ángel González Prieto, Eva Miranda, and Daniel Peralta-Salas, focusing on the study of plugs. Following his thesis, he participated in the Wolfram Summer School, where he worked on simulations related to Topological Kleene Field Theories (TKFTs).

His research lies at the intersection of geometry, fluid dynamics, and computer science. More specifically, he explores the application of topological and geometrical techniques—particularly from Contact and Symplectic Geometry and Topological Quantum Field Theories (TQFTs)—to fluid dynamics, with an emphasis on their connections to computational complexity. 

You can check some of his work here: https://community.wolfram.com/groups/-/m/t/3497702