Geometric field theory began in the 1970’s, following the success of symplectic geometry and propelled by the construction of the standard model of particle physics.

We are leading the development of geometric field theory, with the objective of realizing its full potential by recovering the fecund connections with physics. We are particularly interested in providing the mathematical artillery necessary to solve the challenges posed by theoretical cosmology. As history teaches us, this requires an interdisciplinary approach between the two disciplines.

Integrability is a set of techniques used to characterize the space of solutions of certain dynamical systems, including finding exact solutions.

We are expanding the integrability results to more general situations. We aim to provide stronger tools to better understand the stability and other properties of novel physical models.

In recent years, a large number of modifications of general relativity have been put forward to explain cosmological observations.

We are using geometric techniques to characterize and classify these models, and to elucidate their formal agreement with observation. We are also investigate the physical validity of the geometric-motivated action-dependent gravity.

Quantum field theory is a highly successful theory. Nevertheless, the difficulty of unifying it with General Relativity and the lack of an agreed-upon axiomatization calls for a deeper comprehension of its foundations.

We study alternative theories to non-relativistic quantum mechanics with the goal of constraining the space of quantum mechanical theories. We are working on modifications of quantum mechanics based on the real numbers and on the quaternions, as well as the description of exotic phases of matter like topologically ordered quantum phases.