KTH/SU Mathematics Colloquium

06-10-25

Arnfinn Laudal, University of Oslo

Dynamics of Time-spaces. Chronos and the Demiurge

This year at the Institute Mittag-Leffler is devoted to moduli theory. The notion of moduli, introduced by Riemann, referred to the parameters needed to distinguish isomorphism classes of analytic structures on a Riemannian surface of genus g. There are 3g-3 such moduli. Reformulated and developed by Grothendieck and Mumford, moduli theory is today a central theme in mathematics and mathematical physics.

In this, expository talk, I shall show that there are mathematical models for some interesting physical systems, in which time comes up as a metric on the moduli space of the objects we study. The dynamics is then formulated in terms of, a canonical derivation of the ring of observables, Lagrangians or force laws, and parsimony. If time permits, I shall, as examples, take a quick look at the harmonic oscillator and classical electromagnetism.