Exceptional Lie Algebras at the very Foundations of Space and Time

While describing the results of our recent work on exceptional Lie and Jordan algebras, so tightly intertwined in their connection with elementary particles, we will try to stimulate a critical discussion on the nature of spacetime and indicate how these algebraic structures can inspire a new way of going beyond the current knowledge of fundamental physics.
Comment: Talk presented by P.T. at the Conference 'Group Theory, Probability, and the Structure of Spacetime' in honor of V.S.Varadarajan, UCLA Department of Mathematics, November 7--9, 2014. To appear in a special issue of 'p-Adic Numbers, Ultrametric Analysis and Applications' . Comments welcome