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Almgren–Pitts min-max theory; Approximation theory; Arakelov theory; Asymptotic theory; Automata theory; Bass–Serre theory; Bifurcation theory; Braid theory; Brill–Noether theory; Catastrophe theory; Category theory; Chaos theory; Character theory; Choquet theory; Class field theory; Cobordism theory; Coding theory; Cohomology theory ...
Orchestrated objective reduction (Orch OR) is a theory postulating that consciousness originates at the quantum level inside neurons (rather than being a product of neural connections). The mechanism is held to be a quantum process called objective reduction that is orchestrated by cellular structures called microtubules .
The implication is that a quantum field theory on noncommutative spacetime can be interpreted as a low energy limit of the theory of open strings. Two papers, one by Sergio Doplicher , Klaus Fredenhagen and John Roberts [ 5 ] and the other by D. V. Ahluwalia, [ 6 ] set out another motivation for the possible noncommutativity of space-time.
Other generalizations of Riemannian geometry include Finsler geometry. There exists a close analogy of differential geometry with the mathematical structure of defects in regular crystals. Dislocations and disclinations produce torsions and curvature. [2] [3] The following articles provide some useful introductory material: Metric tensor
There are many examples of coherent/geometric theories: all algebraic theories, such as group theory and ring theory, all essentially algebraic theories, such as category theory, the theory of fields, the theory of local rings, lattice theory, projective geometry, the theory of separably closed local rings (aka “strictly Henselian local rings ...
Supergeometry is differential geometry of modules over graded commutative algebras, supermanifolds and graded manifolds.Supergeometry is part and parcel of many classical and quantum field theories involving odd fields, e.g., SUSY field theory, BRST theory, or supergravity.
In a topos mathematics can be done. In a higher topos not only mathematics can be done but also "n-geometry", which is higher homotopy theory. The topos hypothesis is that the (n+1)-category nCat is a Grothendieck (n+1)-topos. Higher topos theory can also be used in a purely algebro-geometric way to solve various moduli problems in this setting.
In collapse theories, the Schrödinger equation is supplemented with additional nonlinear and stochastic terms (spontaneous collapses) which localize the wave function in space. The resulting dynamics is such that for microscopic isolated systems, the new terms have a negligible effect; therefore, the usual quantum properties are recovered ...