Graphs on Surfaces and Their Applications

By Sergei K. Lando, A. Zvonkin. 2003

910 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/4e5200cffd762239e11a1e93f3aad556c2c5ca69

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In Computational Theory and Mathematics

Citations in the corpus

Thistlethwaite's theorem for virtual links (2007, background): “There are several books on this subject and its applications [GT, LZ , MT].”
Classical Hurwitz numbers and related combinatorics (2016, background): “The second one is the enumeration of ribbon graphs (aka Grothendieck’s dessins d’enfants) [3, 29, 36].”
A view from infinity of the uniform infinite planar quadrangulation (2012, background): “They also appear in various areas, such as algebraic geometry [23], random matrices [37] and theoretical physics, where they have been used as a model of random geometry [2].”
Scaling limits of random trees and planar maps (2011, background): “Graphs drawn on surfaces also have important algebraic and geometric applications; see the book [27].”
An algebro-geometric proof of Witten's conjecture (2006, background): “e KdV equation ∂U ∂t 1 = U ∂U ∂t 0 + 1 12 ∂3U ∂t3 0 . (2) The motivation for this conjecture can be found in [23], and for a detailed exposition suitable for a mathematically-minded reader see, e.g., [14]. Note that the KdV equation can be interpreted as a reccurence formula allowing one to calculat”
Local Convergence of Large Critical Multi-type Galton–Watson Trees and Applications to Random Maps (2014, background): “These objects were first studied from a combinatorial point of view in the works of Tutte in the 1960s (see for example [30]), and have since been of use in different domains of mathematics, such as algebraic geometry (see for example [17]) and theoretical physics (as in [3]).”
Weighted Hurwitz Numbers and Topological Recursion (2018, methodology): “1 Constellations and branched covers We give here another interpretation of τ (t, s) as generating function of certain embedded weighted, bipartite graphs on surfaces (introduced in [58]), called constellations.”
Elliptic Surfaces (2009, background): “In this respect, the dessins d’enfant could be regarded as intermediate between the other two (see for instance [44] for details).”
Uniqueness and universality of the Brownian map (2011, background): “ince the pioneering work of Tutte [28], planar maps have been studied thoroughly in combinatorics, and they also arise in other areas of mathematics: See, in particular, the book of Lando and Zvonkin [12] for algebraic and geometric motivations. Large random planar graphs are of interest in theoreti”
Solution of the polynomial moment problem (2007, background): “ion is deﬁned uniquely up to a choice of P−1 1 (z). The tree constructed above is known under the name of “constellation” or “cactus” and is closely related to what is called a “dessin d’enfant” (see [15] for further details and other versions of this construction). Notice that the Riemann existence”
Expanding Thurston Maps (2010, background): “See [LZ04] for an introduction to this subject.”
Mutant knots and intersection graphs (2007, methodology): “Below, we use standard notions of the theory of finite order, or Vassiliev, invariants of knots in 3-space; their definitions can be found, for example, in [6] or [14].”
Monotone Hurwitz Numbers in Genus Zero (2012, background): “The transitivity condition for the factorization translates to the requirement that the corresponding cover is connected .”