Non|Euclidean geometry in nLab
geometric quantization in nLab
a Hilbert space of states as the space of sections of the associated line bundle which depend only on the “coordinates” (not on the “momenta”);.
generalized complex geometry in nLab
This geometry of symplectic Lie 2-algebroids turns out to unify, among other things, complex geometry with symplectic geometry. This unification ...
multisymplectic geometry in nLab
Multisymplectic geometry is a generalization of symplectic geometry in the context of variational calculus and mechanical systems in which the ...
(2,1)-dimensional Euclidean field theories and tmf in nLab
3. References. Stephan Stolz, Peter Teichner, What is an elliptic object? in Topology, geometry and quantum field theory , London Math. Soc ...
This terminological mismatch is quite stark in the main application to homotopy theory, where one cares only about the (weak) homotopy type of ...
5. Related concepts ... Orbifolds are in differential geometry what Deligne-Mumford stacks are in algebraic geometry. See also at geometric ...
Much geometric information is contained in these D-brane states, and the resulting concept of (noncommutative) geometry has accordingly been ...
nLab descent in noncommutative algebraic geometry
In that case, Grothendieck essentially used the symmetry in commutative case. Another problem is that localizations are hard to find, especially ...
arithmetic differential geometry in nLab
24). However, in the case of multiple primes Borger requires Frobenius lifts to commute, and this diverges from the non-vanishing 'curvature' ...
derived analytic geometry in nLab
Derived analytic geometry is the study of derived analogs of analytic spaces in various context, such as complex analytic geometry, non-archimedean analytic ...
nLab quantum Hall effect via noncommutative geometry -- references
Vincent Pasquier: Quantum Hall Effect and Non-commutative Geometry, in: Quantum Spaces, Progress in Mathematical Physics 53, Birkhäuser (2007) [ ...
Connes-Lott-Chamseddine-Barrett model in nLab
Alain Connes, Gravity coupled with matter and foundation of non-commutative geometry, Commun.Math.Phys. 182 (1996) 155-176 (arXiv:hep-th ...
T-duality and (related) mirror symmetry interchange the symplectic data and complex algebraic geometry data. Some cases of both the symplectic ...
complex analytic geometry is closely related to algebraic geometry over the complex numbers. See at GAGA for more on this. 3. Related concepts.
geometric Langlands correspondence in nLab
for L G {}^L G the Langlands dual group. Moreover, the conjecture asserts that there is canonical such an equivalence which is a non-abelian ...
derived algebraic geometry in nLab
The hidden smoothness principle of Maxim Kontsevich, which conjectures that in classical algebraic geometry, the non-smoothness? of certain ...
The functor which sends R R to the R R -points of the projective space ℙ n \mathbb{P}^n corresponds to a non-affine scheme. 3. Value added by ...
geometry of physics -- perturbative quantum field theory in nLab
below). But we aim to organize all concepts such that the structure of their generalization to curved spacetime and non-trivial field bundles is immediate. This ...
we work with functions on “manifolds” but the functions do not necessarily converge, the geometry is rather based on topological algebras of ...
... geometry in statistical inference (project Euclid). Shun-ichi Amari, Information geometry and its applications, Applied Mathematical Sciences ...
Analytic geometry
Field of studyIn mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.
Differential geometry
DisciplineDifferential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds.
Euclidean space
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's Elements, it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension n, which are called Euclidean n-spaces when one wants to specify their dimension.
Projective geometry
Field of studyIn mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations.
Pythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.
Elliptic geometry
Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect.