I am a theoretical physicist at the Instituto de Ciencias Nucleares of the UNAM in Mexico City. 
I studied physics at Julius-Maximilians-Universität Würzburg and the University of Texas at Austin and I received my PhD from Universität Würzburg in 2008. From 2008 to 2012 I was a postdoc at Perimeter Institute for Theoretical Physics in Waterloo, Ontario, and a member of the quantum gravity group and from 2012 to 2015 I was postdoc in the quantum gravity group at the University of New Brunswick in Fredericton. Previously, I have worked on various approaches to quantum gravity, whichever seemed most promising at the time. In particular, I have worked on canonical loop quantum gravity, loop quantum geometry condensate, exact renormalization group methods and matrix models. My current main research interest since 2011 is mainly focused on the shape dynamics description of gravity, which describes gravity not in terms of geometry of spacetime, but as an equation of state of a curve in conformal superspace. This description of gravity that instead implements the idea that there is no absolute local scale as has long been advocated by Julian Barbour and has lead to some new insights about the nature of gravity, in particular the revelation of a gravitational arrow of time, the evolution through spacetime singularities and has laid new foundations for the search for quantum gravity. Besides shape dynamcis I am currently working on the application of the functional renormalization group equation to discrete models of gravity and on foundational aspects of quantum theories. 

Shape dynamics is a mathematical a description of gravity that makes the same experimental predictions as general relativity, but is built from very different principles: General relativity is describes gravity as curvature of spacetime geometry and spacetime symmetry, but fails to satisfy Mach's principle, because the predictions of general relativity depend on the choice of external clocks and rods that are used in its interpretation.
Shape Dynamics implements Mach's principle by describing gravity as evolution of spatial "shapes" (precisely: spatial conformal geometry). This change in perspective changes has profound implications in the search for quantum gravity, because it implies that quantum gravity could be found by searching for a quantum field theory built form purely Machian ideas. Moreover, shape dynamics allows us to attack a number of difficult problems in classical and quantum gravity with new tools. These are in particular the problem of observables and the closely related problem of time in quantum gravity, which is absent in shape dynamics.

Loop quantum geometry condensate or loop quantum gravity with background geometry is a version of loop quantum gravity that evades the famous F/LOST uniqueness theorem because it violates some technical assumptions whose physical meaning is questionable. This allowed me to construct a version of loop quantum gravity that has a classical spatial background geometry with loop quantum fluctuations thereon. This version of loop quantum gravity has features similar to a Bose condensate and Hanno Sahlmann suggested that it should be used for effective field theory.
Exact renomalization group in quantum gravity is mainly applied in the context of the asymptotic safety scenario. Proving asymptotic safety in quantum gravity seems out of the reach of current methods. Alessandro Sfondrini and myself tested this method and showed  how exact renormlization group methods can be used to prove asymptotic safety of the Grosse-Wulkenhaar model. I also used these methods to study the IR effects of preferred foliations in quantum gravity.