Interview With Alain Connes | Not Even Wrong →
RÉSONAANCES: Alain Connes' Standard Model →
Spaces can be characterized by their algebras of functions. Using this duality between space and quantity one can define generalized spaces in terms of generalizations of their algebras of functions. The idea of noncommutative geometry is to encode everything about the geometry of a space algebraically and then allow all commutative function algebras to be generalized to possibly non-commutative...
noncommutative geometry in nLab →
Noncommutative Geometry [PDF] 4.1 MB Academic Press, San Diego, CA, 1994, 661 p., ISBN 0-12-185860-X. Noncommutative Geometry, Quantum Fields and Motives [PDF] 6.4 MB With Matilde Marcolli Preliminary version still under revision. Complete List of Downloadable Papers http://www.alainconnes.org/en/downloads.php
Alain Connes is one of the leading specialists on...
Visual test linked to high IQ →
High IQ folks can’t see the big picture, a visual perception study suggests, pointing to a view of intelligence that sees screening out irrelevant details as the key to smarts.
Eric Weinstein on Geometric Unity | Not Even Wrong →
Roll over Einstein: meet Weinstein
http://www.guardian.co.uk/science/2013/may/23/eric-weinstein-answer-physics-problems http://www.guardian.co.uk/science/blog/2013/may/23/roll-over-einstein-meet-weinstein P.S. Probably hype!!—-GGD
Alan Weinstein, Symplectic geometry →
THE SYMPLECTIZATION OF SCIENCE: Symplectic... →
Physics is geometry. This dictum is one of the guiding principles of modern physics. It largely originated with Albert Einstein, whose most important contribution–via his General Theory of Relativity–was to view the phenomenon of gravity as a reflection of the curvature of the geometry of spacetime. Einstein’s vision is remarkable in its simplicity, has great conceptual power and is physically...
Symplectic Geometry is a branch of differential geometry and differential topology which studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry has its origins in the Hamiltonian formulation of classical mechanics where the phase space of certain classical systems takes on the structure of a symplectic manifold. Symplectic...
Arnold can be said to have initiated the theory of symplectic topology as a distinct discipline. The Arnold conjecture on the number of fixed points of Hamiltonian symplectomorphisms and Lagrangian intersections were also a major motivation in the development of Floer homology. http://en.wikipedia.org/wiki/Vladimir_Arnold