I am a mathematician working in the areas of partial differential equations, dynamical systems, and the calculus of variations, with applications to problems in soft matter physics. My research develops and analyzes mathematical models that describe how complex materials organize, evolve, and respond to physical constraints. As an undergraduate, I received my training in mathematics and physics from the University of Barcelona and obtained my PhD in mathematics from Heriot-Watt University (Edinburgh, UK)
A central theme of my work is the study of liquid crystals, which offer a rich setting for exploring nonlinear phenomena. I investigate how confinement, geometry, and boundary conditions determine equilibrium and dynamical behaviors, including the formation of defects and other topologically constrained structures. These questions connect naturally to energy minimization, pattern formation, and geometric analysis. Recent projects have addressed colloidal and ferromagnetic systems, ferroelectric liquid crystals, electrokinetic flow, solitons, and active liquid crystals. The latter is part of my broader investigation of active matter —such as suspensions of self-propelled or living particles —drawing on concepts from fluid mechanics and viscoelastic flow.
In another research direction, I study the geometric and topological arrangement of DNA under confinement, both in-vitro and inside viral capsids, where the competition of elastic, electrostatic and entropic forces play cruzial roles. In collaboration with experimentalists, we have focused on studies of bacteriophage viruses, using nonlinear analysis and topological methods to understand how DNA is packed and released during infection. In particular, we have characterized the density, type and complexity of knots in confined DNA and their relation with mechanical and ionic effects. This line of research bridges rigorous mathematics with biological mechanisms, showing how topology and analysis can illuminate the physics of soft and living mattept?r.
Another aspect of my work addresses the mechanics of gels and soft solids, including liquid crystal elastomers. In one of our themes, we study the debonding of thin films from substrates by applying tools from solid fracture to soft materials, leading to models that capture the interplay between adhesion forces and large elastic deformation. This research combines calculus of variations, numerical simulations, and laboratory experiments to elucidate how delamination patterns arise in gel systems. Related studies include the formation and evolution of Schallamach waves —surface slip pulses observed in soft adhesives —in connection to the design of earthquake-protective materials.
Together, these studies highlight how variational and dynamical frameworks can connect mathematical theory with physical modeling and practical applications in soft matter and materials science.
Another topic of my research interest is the study of the structure of water at interfaces with highly charged polymers, such as Nafion, and proteins, in order to explain some unusual properties of an observed water layer of the order of 100 nm in thickness.
Above all, I find great satisfaction in teaching, mentoring and in helping students, at all levels, appreciate the unifying role of mathematics across the sciences.
