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Tate conjecture: algebraic geometry: John Tate: Toeplitz' conjecture: Jordan curves: Otto Toeplitz: Tuza's conjecture: graph theory: Zsolt Tuza: Twin prime conjecture: number theory: n/a: 1700 Ulam's packing conjecture: packing: Stanislaw Ulam: Unicity conjecture for Markov numbers: number theory: Andrey Markov (by way of Markov numbers ...
Sometimes, a conjecture is called a hypothesis when it is used frequently and repeatedly as an assumption in proofs of other results. For example, the Riemann hypothesis is a conjecture from number theory that — amongst other things — makes predictions about the distribution of prime numbers. Few number theorists doubt that the Riemann ...
In the mathematical field of geometric topology, the Poincaré conjecture (UK: / ˈ p w æ̃ k ær eɪ /, [2] US: / ˌ p w æ̃ k ɑː ˈ r eɪ /, [3] [4] French: [pwɛ̃kaʁe]) is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space.
The Tate conjecture (John Tate, 1963) provided an analogue to the Hodge conjecture, also on algebraic cycles, but well within arithmetic geometry. It also gave, for elliptic surfaces , an analogue of the Birch–Swinnerton-Dyer conjecture (q.v.), leading quickly to a clarification of the latter and a recognition of its importance.
In 2001, the proof of the local Langlands conjectures for GL n was based on the geometry of certain Shimura varieties. [27] In the 2010s, Peter Scholze developed perfectoid spaces and new cohomology theories in arithmetic geometry over p-adic fields with application to Galois representations and certain cases of the weight-monodromy conjecture ...
The Riemann hypothesis is one of the most important conjectures in mathematics.It is a statement about the zeros of the Riemann zeta function.Various geometrical and arithmetical objects can be described by so-called global L-functions, which are formally similar to the Riemann zeta-function.
Hodge conjecture for Kähler varieties, vector bundle version. Let X be a complex Kähler manifold. Then every Hodge class on X is a linear combination with rational coefficients of Chern classes of vector bundles on X. Hodge conjecture for Kähler varieties, coherent sheaf version. Let X be a complex Kähler manifold.
A model geometry is a simply connected smooth manifold X together with a transitive action of a Lie group G on X with compact stabilizers. A model geometry is called maximal if G is maximal among groups acting smoothly and transitively on X with compact stabilizers. Sometimes this condition is included in the definition of a model geometry.