Foundations of the Exact Science

From the birth of science, mathematics and physics have played a major role and their evolution has always been closely connected. Pythagoras, Aristotle, Ezeno, Euclid, Archimedes, etc . . . till our times, Riemann, Hilbert, Einstein, Poincare, Heisenberg, Schrodinger, Dirac, Von Neumann, Godel, etc . . . Have all wandered between mathematics and theoretical physics, investigating the fundamental scientific problems of their times. In this tradition, FUND investigates today's fundamental problems, more specifically the conceptual, mathematical, axiomatic and logical foundations of physics. Current research topics are : 1. Study of the mathematical structures (algebra's probality models, logics, categorical structures, close structure, ortho structure) that are relevant for modern axiomatic quantum theory. 2. The problems that are connected to the description of compound entities (existence and construction of co-products in the categories connected to the different structures) 3. Quantum axiomatics (the fundamental representation theorem, projective structures that are connected to this problem, generalised Hilbert spaces) 4. Foundations of physics, especially quantum mechanics and relativety theory: measurements problem, non-locality and the origin of space-time structures, the quantum and relativity paradoxes, operational foundations of the mathematical structures. 5. New quantum experiments on individual quantum entities: atom, neutron and photon delocalisation and interference experiments. The role of time in quantum theory. Description of 'between quantum and classical' intermediate situations and of entangled and separated entities. Connections with EPR paradox.