Mathcenter Forum - Maryam Mirzakhani

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26 พฤษภาคม 2020 14:25

Maryam Mirzakhani

Maryam Mirzakhani
(Persian: 12 May 1977 – 14 July 2017) was an Iranian[1][5][6][7]mathematician
and a professor of mathematics at Stanford University.[8][9][10]

Her research topics included
Teichmüller theory, hyperbolic geometry,
ergodic theory, and symplectic geometry.[1]

Wiki

10 กันยายน 2020 14:46

Ergodic theory is a branch of mathematics that studies statistical properties of
deterministic dynamical systems.
In this context, statistical properties means properties which are expressed through the behavior of time averages of various functions along trajectories of dynamical systems.

The notion of deterministic dynamical systems assumes that
the equations determining the dynamics do not contain
any random perturbations, noise, etc.
Thus, the statistics with which we are concerned are properties of the dynamics.

Ergodic theory, like probability theory, is based on general notions of measure theory.
Its initial development was motivated by problems of statistical physics.

10 กันยายน 2020 14:50

Symplectic geometry is a branch of differential geometry and differential topology
that 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.[1]
Wiki

10 กันยายน 2020 15:15

Hyperbolic geometry (also called Lobachevskian geometry or
Bolyai–Lobachevskian geometry) is a non-Euclidean geometry.
The parallel postulate of Euclidean geometry is replaced with:

For any given line R and point P not on R,
in the plane containing both line R and
point P there are at least two distinct lines through P that do not intersect R.
(compare this with Playfair's axiom, the modern version of
Euclid's parallel postulate)

Hyperbolic plane geometry is also the geometry of saddle surfaces and pseudospherical surfaces, surfaces with a constant negative Gaussian curvature.

A modern use of hyperbolic geometry is in the theory of special relativity, particularly Minkowski spacetime and gyrovector space.

22 มกราคม 2021 08:43

In mathematics, the Teichmüller space T(S) of a (real) topological (or differential) surface S,
is a space that parametrizes complex structures on S up to the action of homeomorphisms
that are isotopic to the identity homeomorphism.

Each point in T(S) may be regarded as an isomorphism class of "marked" Riemann surfaces,
where a "marking" is an isotopy class of homeomorphisms from S to itself.

Wiki

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