In general, my scientific interests are mainly concentrated around design and analysis of dynamics on discrete spaces. The model, at the heart of the subject, is a graph, appearing in different forms, from abstract graphs to more geometric ones as metric-measure spaces. Also, the dynamics on such spaces cover a vast area of applications, from algorithms as discrete dynamics to networks as geometric objects or microscopic physical models of real materials. These are the main motivations for my interest in this intersection of mathematics, computer science, and physics.

I cannot resist recalling the following quote (see [Geometry and the Quantum] by Alain Connes):

In the prelude of “Récoltes et Semailles", Alexandre Grothendieck makes the following points on the search for
relevant geometric models for physics and on Riemann’s lecture on the foundations of geometry. 

"It must be already fifteen or twenty years ago that, leafing through the modest volume constituting the complete works of Riemann, I was struck by a remark of his “in passing”. He pointed out that it could well be that the ultimate structure of space is discrete, while the continuous representations that we make of it constitute perhaps a simplification (perhaps excessive, in the long run ...) of a more complex reality; That for the human mind, “the continuous” was easier to grasp than “the discontinuous”, and that it serves us, therefore, as an “approximation” to apprehend the discontinuous.

This is a remark of a surprising penetration in the mouth of a mathematician, at a time when the Euclidean model of physical space had never yet been questioned; in the strictly logical sense, it is rather the discontinuous which traditionally served as a mode of technical approach to the continuous.

Mathematical developments of recent decades have, moreover, shown a much more intimate symbiosis between continuous and discontinuous structures than was imagined, even in the first half of this century. ..."