My research interests are diverse and dynamic, but they all organically fit into what I characterize as "Fundamental Physics." I believe the best definition of this discipline, which is certainly not a specific specialized field, is given by Einstein in the quote attributed to him by a student:

Research projects currently underway:

• Complete formulation of the Pure Shape Dynamics approach to Quantum Field Theory (in collaboration with Tim Koslowski):

The tenets of Pure Shape Dynamics require that a closed and autonomous dynamical system, consisting solely of the relational, scale-less part of the configuration in any model, that is, the "shape." In the case of quantum fields, one may work with either a field ontology or a particle ontology. In either case, one must identify the corresponding shape degrees of freedom and construct the dynamics on that shape space. What QFT additionally brings forth is that any model must be regularized with respect to an intrinsic physical scale, without invoking a general external high-energy cutoff, irrespective of the specific physics involved. In other words, the universe and the structures within it themselves establish the "fine" scale according to which the quantum fields can vary. Implementation of all these principles yields a well-defined, finite framework of models for QFT on shape space.

• General Relativity without Dynamical "Geometry":

Since Newton and his formulation of mechanics, geometry has become an indispensable element of mathematical physics. In classical physics, geometry was always fixed as a background against which different physical models were constructed. Einstein revolutionized this approach by making geometry, as championed by him, a dynamical field coupled to all the other matter fields in his theory of General Relativity.

From a relational perspective, I find both approaches (background and dynamical) to geometry unsatisfactory and conceptually tainted. This view is based on the physical realization that geometry always refers to the "structure of matter" and not to an entity independent and separate from it. Let us recall the etymology of geometry in this connection, that is, "measuring earth", the same physical earth which we observe and model as a material configuration in physics. Therefore, I strongly believe that a truly relational theory must only recognize the geometrical structure of matter, and kinematically espouse a notion of "emergent geometry" from matter. This means that we should endorse a fundamental ontology of the universe based on geometric shapes of material structures with no external reference or dynamical coupling to a geometry, to which we then assign an observable effective geometry. Successful completion of such an approach would present the challenge of developing a well-defined dynamics that reproduces the empirically verified solutions to GR but with no dynamical geometry.

• Philosophical investigations in PSD approach to Dynamical Geometry and the notion of Shape Space (in collaboration with Antonio Vassallo)

Side quests:

• Methodological foundation of science and a comparative study of Galileo (in collaboration with Pedro Naranjo):

We are most certainly living through a crisis in science. There is little doubt about that. There have been no major theoretical breakthroughs or novel, groundbreaking empirical discoveries for more than six decades. As part of understanding the source of this crisis, I was led to question the very methodology of science, or at least those recognizable aspects thereof that have stably formed and congealed within the scientific enterprise. I surmise that the current crisis is more methodological than merely theoretical. This research continues the thread back to the inception of scientific practice with Galileo. The aspiration is, first, to identify the invariant, minimal methodology despite several revolutions and fundamental changes in the history of science, and then to go further by proposing an alternative method in broad strokes.

• What grounds the universal unity and "objectivity" in relationalism

A question that arises in the relational-perspectival approach is whether there exists a unique universe that embeds and unifies all relations. The importance of this question lies in the following: If we posit the fundamental reality of perspectives and treat properties as relational, the issue that naturally follows is whether these properties can be consistently fit into a single universe. How are we all sure that we live in the same universe and talk about the same set of facts that are objectively real outside our individual perceptions? In Leibnizian terms, how do we know that all "micro-cosms" that see the universe from within reside within one cosmos?

In a minimal model of relationalism for points equipped with angle geometry, this question can be formulated in terms of the necessary and sufficient conditions required for the embeddability of the shape into a space of sufficiently low dimension. This line of investigation leads to important questions regarding the origin of three dimensions, the geometry of space, topology, and related issues. All of these problems ultimately stem from the original question: What is the irreducible structure in the relational universe that grounds the objectivity of perspective, that is, the uniqueness of the universe which individual perspectives experience?