particularly in representation theory, a symplectic resolution is a morphism that combines symplectic geometry and resolution of singularities. Let π : Y → X {\displaystyle...

Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds...

properties and concepts in symplectic geometry in mathematics. The terms listed here cover the occurrences of symplectic geometry both in topology as...

bundles are vector bundles of rank n ! {\displaystyle n!} on certain symplectic resolutions of quotient singularities, particularly on the Hilbert scheme of...

the maxilla itself located further back, and an additional bone, the symplectic, linking the jaw to the rest of the cranium. Although the skulls of fossil...

position. The second strength is its symplectic nature, which implies that it conserves the (slightly modified; see symplectic integrator) energy of a Hamiltonian...

symplectic summation, is the symplectic analogue of deformation to the normal cone along a smooth divisor. Infinitely near point Resolution of singularities Fulton...

manifold is a Riemannian manifold whose holonomy group is contained in the symplectic group. This condition on a Riemannian manifold may also be characterized...

the momentum equation. Other symplectic integrators exist (see the reference textbook). It is recommended to use a symplectic (even low-order) scheme instead...

the triangle, in this case). Note that this construction is related to symplectic geometry as the map { C P 2 → R ≥ 0 ( z 1 , z 2 , z 3 ) ↦ | z 1 | + |...

state of a classical system. The canonical structure (also known as the symplectic structure) of classical mechanics consists of Poisson brackets enclosing...

included Teichmüller theory, hyperbolic geometry, ergodic theory, and symplectic geometry. On 13 August 2014, Mirzakhani was honored with the Fields Medal...

linear transforms of the time–frequency representation that preserve the symplectic form. These include and generalize the Fourier transform, fractional Fourier...

2017. Retrieved May 16, 2018. Wisdom, Jack; Holman, Matthew (1991). "Symplectic maps for the n-body problem". Astronomical Journal. 102: 1528–1538. Bibcode:1991AJ...

special linear group SL2(R) on the time–frequency plane, with the preserved symplectic form corresponding to the uncertainty principle, below. This approach...

enough derivatives. Applications, according to Arnold, are to be seen in symplectic geometry, as the geometric form of classical mechanics. An important reason...

self-avoiding walks Arnold–Givental conjecture and Arnold conjecture – relating symplectic geometry to Morse theory. Berry–Tabor conjecture in quantum chaos Banach's...

formulated by symplectic manifold, observables are real-valued functions on it, time evolution is given by a one-parameter group of symplectic transformations...

important results in geometry and topology, particularly in the field of symplectic geometry and pseudo-holomorphic curve, which are certain types of smooth...

mathematician, specializing in algebraic geometry, differential geometry, and symplectic geometry with applications to string theory. Ruan studied from 1978 at...

Paulette Libermann (1919-2007) he published in 1987 a research-level book on symplectic geometry and geometric mechanics. He has recently published another book...

Belarusian-American mathematician, specializing in representation theory, symplectic geometry, algebraic geometry, and combinatorial algebra. Losev matriculated...

r} first class constraints Φ i {\displaystyle \Phi _{i}} acting upon a symplectic space M {\displaystyle M} . M 0 {\displaystyle M_{0}} is the submanifold...

Pseudoholomorphic curves were shown by Mikhail Gromov in 1985 to be powerful tools in symplectic geometry. In 1991, Edward Witten conjectured a use of Gromov's theory...

{\displaystyle A} . This symplectic form is the Atiyah–Bott symplectic form first discovered by Atiyah and Bott. Using this symplectic form, Atiyah and Bott...

theory, topology, computational complexity theory, integral geometry, symplectic geometry, partial differential equations (geometry of wavefronts), complex...

groundbreaking work relating to Seiberg-Witten and Gromov-Witten invariants of symplectic 4-manifolds, and his proof of Weinstein conjecture for all contact 3-manifolds...

methods are especially designed for special classes of ODEs (for example, symplectic integrators for the solution of Hamiltonian equations). They take care...

{\displaystyle X} and velocity V {\displaystyle V} may be integrated with a symplectic integrator method such as Verlet integration. The time evolution of X...

the geometry of classical mechanics and field theory, especially the symplectic and multisymplectic structures that underlie the Hamiltonian and Lagrangian...