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.