In algebraic geometry, the Witten conjecture is a conjecture about intersection numbers of stable classes on the moduli space of curves, introduced by Edward Witten in the paper Witten (1991), and generalized in Witten (1993).
Witten's original conjecture was proved by Maxim Kontsevich in the paper Kontsevich (1992).
Witten's motivation for the conjecture was that two different models of 2-dimensional quantum gravity should have the same partition function. The partition function for one of these models can be described in terms of intersection numbers on the moduli stack of algebraic curves, and the partition function for the other is the logarithm of the τ-function of the KdV hierarchy. Identifying these partition functions gives Witten's conjecture that a certain generating function formed from intersection numbers should satisfy the differential equations of the KdV hierarchy.
Edward Witten (born August 26, 1951) is an American theoretical physicist known for his contributions to string theory, topological quantum field theory...
international meeting, the Arbeitstagung, where he sketched a proof of the Wittenconjecture to the amazement of Michael Atiyah and other mathematicians and his...
easily using Seiberg–Witten theory, though there are a number of open problems remaining in Donaldson theory, such as the Wittenconjecture and the Atiyah–Floer...
construction of Pin (2)-equivariant Seiberg–Witten Floer homology, with which he disproved the Triangulation Conjecture for manifolds of dimension 5 and higher...
statement of the problem was given by Arthur Jaffe and Edward Witten. Mathematics portal Beal conjecture Hilbert's problems List of mathematics awards List of...
In algebraic geometry, the Virasoro conjecture states that a certain generating function encoding Gromov–Witten invariants of a smooth projective variety...
Weinstein conjecture has now been proven for all closed 3-dimensional manifolds by Clifford Taubes. The proof uses a variant of Seiberg–Witten Floer homology...
Frenkel-Lepowsky-Meurman's conjecture that moonshine module is the unique holomorphic VOA with central charge 24 and character j-744, Witten concluded that pure...
Edward Witten suggested that the five theories were just special limiting cases of an eleven-dimensional theory called M-theory. Witten'sconjecture was...
the first Chern classes of the n cotangent line bundles, as in Witten'sconjecture. Let a 1 , … , a n {\displaystyle a_{1},\ldots ,a_{n}} be positive...
using the Seiberg–Witten invariants. There is at least one generalization of this conjecture, known as the symplectic Thom conjecture (which is now a theorem...
MR 1798809 Taubes, Clifford Henry (2007), "The Seiberg-Witten equations and the Weinstein conjecture", Geometry & Topology, 11 (4): 2117–2202, arXiv:math/0611007...
Serre's modularity conjecture Standard conjectures on algebraic cycles Abramovich, Dan; Graber, Tom; Vistoli, Angelo (2008). "Gromov-Witten Theory of Deligne-Mumford...
Langlands correspondence is related to important conjectures in number theory such as the Taniyama–Shimura conjecture, which includes Fermat's Last Theorem as...
and partly motivated Witten's introduction of the Seiberg–Witten invariants. The second paper proves the so-called Thom conjecture and was one of the first...
In mathematics, the Weil conjectures were highly influential proposals by André Weil (1949). They led to a successful multi-decade program to prove them...
medal as of 2022. With the exception of two PhD holders in physics (Edward Witten and Martin Hairer), only people with a PhD in mathematics have won the medal...
ELSV formula, including the Wittenconjecture, the Virasoro constraints, and the λ g {\displaystyle \lambda _{g}} -conjecture. It is generalized by the...
1985 to be powerful tools in symplectic geometry. In 1991, Edward Wittenconjectured a use of Gromov's theory to define enumerative invariants. Tian and...
Maulik–Nekrasov–Okounkov–Pandharipande conjecture on an equivalence between Gromov–Witten theory and Donaldson–Thomas theory Nagata's conjecture on curves, specifically...
students included Graeme Segal, Nigel Hitchin, Simon Donaldson, and Edward Witten. Together with Hirzebruch, he laid the foundations for topological K-theory...
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