http://popups.lib.uliege.be/1373-5411/index.php?id=3471 Index terms fr 0 http://popups.lib.uliege.be/1373-5411/index.php?id=3468 A brief summary of the basic ideas of Topological Geometrodynamics (TGD) is given with a special emphasis on the most recent mathematical developments. There are several first principle approaches to quantum TGD. The basic dynamical objects are light-like 3-surfaces which means a generalization of the conformal symmetries of super string models and implies a parton level formulation of quantum TGD as an almost topological quantum field theory with discrete symplectic fusion algebras playing a key role in the formulation of theory. The notion of finite measurement resolution realized in terms of inclusions of hyperfinite factors of type 111 can be also taken as a fondamental dynamical principle. Associativity -in both number theoretical sense and in the sense of conformal field theories -and number theoretical universality stating that the scattering amplitudes make sense in both real and p-adic number fields define further principles of this kind. All these approaches lead to the notion of number theoretical braid meaning discretization at space-time level. The notion of operad is tailor made for formulating the notion of finite measurement resolution and rather precise formulation of generalized Feynman diagrammatics emerges in this framework. Thu, 19 Sep 2024 15:24:01 +0200 Thu, 19 Sep 2024 15:24:14 +0200 http://popups.lib.uliege.be/1373-5411/index.php?id=3468