Members

Short Biography

Marco Gualtieri is a mathematician working in geometry and mathematical physics, with a focus on developing mathematical structures with applications to quantum field theory. After completing his B. Sc. at McGill University in his native Montreal, he completed his D. Phil. under Nigel Hitchin at the University of Oxford. After research fellowships at the Fields Institute and MIT, he has worked at the University of Toronto since 2008 and at the UPC Barcelona Tech in the SYMCREA lab since 2025. 

Research Interests

Prof. Gualtieri is best-known for his work developing Generalized complex geometry, a type of geometric structure which includes the well known complex geometry and symplectic geometry as extreme special cases, but which includes new geometric structures that we have only recently begun to understand. This study, which grew out of the far-reaching insights of Hitchin and Weinstein, led him to develop Generalized Kähler geometry, a more structured version of the previous geometry which found a surprising application in physics: it coincides with a geometry which was previously proposed by physicists in the study of an important class of quantum field theories. Gualtieri's work has made it possible to find new examples of such models, but also to establish several conjectures made by physicists about their properties.

In addition to the above, Prof. Gualtieri works in Poisson geometry, singular differential equations and is currently exploring models of discrete geometry.

About me

I am ICREA Research Professor at Universitat Politècnica de Catalunya and a member of CRM and IMTECH. 

Throughout my career, I have secured several prestigious grants from the Engineering and Physical Sciences Research Council (EPSRC), including an Advanced Research Fellowship, and from the Leverhulme Trust, for a total of more than two million euro.

Recently, I have been the European Mathematical Society Distinguished Speaker at the Poisson 2024 Conference in Napoli and joined the ArXiv scientific advisory board.

I my previous employment at the University of Birmingham, I created the Geometry and Mathematical Physics group, while here at UPC, together with Eva Miranda and Marco Gualtieri, we created the excellence unit SYMCREA.

My research is mainly in Integrable Systems, an area at the crossroads of many disciplines including Analysis, Geometry, Mathematical Physics and Algebra. My interests include isomonodromic deformations, Frobenius manifolds, (quantum) Teichmüller theory, quantum algebra and mirror symmetry. 

Short Biography

I earned my PhD in Mathematical Physics from the International School for Advanced Studies (SISSA) in Trieste, Italy, in 1998, with a dissertation titled "Algebraic Solutions to the Painlevé-VI Equation and Reflection Groups,”which was published on Inventiones Mathematicae and on Mathematische Annalen. Following my doctoral studies, I held postdoctoral positions at the Mathematical Sciences Research Institute (MSRI) in Berkeley and at the University of Oxford under the supervision of Professor Nigel Hitchin. I later served as a temporary University Lecturer at the University of Cambridge and as a lecturer in Applied Mathematics at the University of Manchester. In 2008, I accepted a readership at Loughborough University, where I was promoted to a personal chair in 2014. In February 2018, I was appointed as a Professor of Mathematics at the University of Birmingham. Finally in 2024, I moved to UPC as ICREA Research Professor.

During my career, I mentored for 4 Phd students as principal supervisor and eight post docs (Guido Carlet, Idan Eisner, Timothy Magee, Giordano Cotti, Livia Campo, Harini Desiraju, Omar Kidwai, Nikita Nikolaev).

About me

I am a Full Professor distinguished with two consecutive ICREA Academia Awards (2016, 2021) at (UPC), member of CRM and IMTECH. I have been recently distinguished with the François Deruyts Prize by the Royal Academy of Belgium and with a Bessel Prize by the Alexander Von Humboldt foundation. I am the 2023 London Mathematical Society Hardy lecturer as such I have enjoyed lecturing a 9 stop-tour in the summer of 2023 which has been quite a unique experience. The picture above was taken in the middle of the tour at the University of Loughborough. Adventure never stops: I have been appointed 2025 Gauss Professor at the University of Goettingen and Nachdiplom lecturer 2025 at ETHZ in Zurich.

I am the director of the Laboratory of Geometry and Dynamical Systems and the group leader of GEOMVAP (Geometry of Varieties and Applications). With Marta Mazzocco we have just created the SYMCREA excellence unit. We are on the third floor at EPSEB. I have been the advisor of 11 PhD students.

My research deals with several aspects of Differential Geometry, Mathematical Physics and Dynamical Systems such as Symplectic and Poisson Geometry, Hamiltonian Dynamics, Group actions and Geometric Quantization. Almost a decade ago I started the investigation of several facets of b-Poisson manifolds (also known as log-symplectic manifolds). These structures appear naturally in physical problems on manifolds with boundary and in Celestial mechanics such as the 3-body problem (and on its restricted versions) after regularization transformations. I recently got interested in Fluid Dynamics and the study of their complexity (computational, topological, logical, dynamical) by looking through a contact mirror unveiled two decades ago by Etnyre and Ghrist.I am currently exploring the connections between dynamical systems and computation. Building on this understanding, we have designed a new model of computation inspired by ideas from Topological Quantum Field Theory (TKFT). One of the problems I am currently working on is to understand undecidable phenomena in physical systems in particular in the three body problem where classical chaos would then meet logical chaos.I am also working in extending Floer homology to the Poisson realm taking as proof of concept simple classes of Poisson manifolds like b-Poisson manifolds and the classical Weinstein conjecture in this set-up. My motivation comes from the search of periodic orbits on regularized problems in Celestial Mechanics (more information here).

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