• Corpus ID: 55394001

Combinatorial description of jumps in spectral networks.

@article{Frolova2015CombinatorialDO,
  title={Combinatorial description of jumps in spectral networks.},
  author={Anastasia Frolova and Alexander Vasil’ev},
  journal={arXiv: Geometric Topology},
  year={2015}
}
We describe a graph parametrization of rational quadratic differentials with presence of a simple pole, whose critical trajectories form a network depending on parameters focusing on the network topological jumps. Obtained bifurcation diagrams are associated with the Stasheff polytopes. 
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Dedication to Alexander Vasil’ev (1962–2016)

References

SHOWING 1-10 OF 25 REFERENCES

Quadratic Differentials and Weighted Graphs on Compact Surfaces

We prove that for every simply connected graph Γ embedded in a compact surface R of genus g≥o, whose edges e i kj carry positive weights w i kj , there exist a complex structure on R and a…

Combinatorial description of a moduli space of curves and of extremal polynomials

For the description of extremal polynomials (that is, the typical solutions of least deviation problems) one uses real hyperelliptic curves. A partitioning of the moduli space of such curves into…

Motivic Donaldson-Thomas invariants: Summary of results

This is a short summary of main results of our paper arXiv:0811.2435 where the concept of motivic Donaldson-Thomas invariant was introduced. It also contains a discussion of some open questions from…

Critical Measures, Quadratic Differentials, and Weak Limits of Zeros of Stieltjes Polynomials

We investigate the asymptotic zero distribution of Heine-Stieltjes polynomials – polynomial solutions of second order differential equations with complex polynomial coefficients. In the case when all…

EQUILIBRIUM DISTRIBUTIONS AND DEGREE OF RATIONAL APPROXIMATION OF ANALYTIC FUNCTIONS

A theorem is proved on the degree of rational approximation of sequences of analytic functions given by Cauchy-type integrals of the form The theorem is formulated in terms connected with the…

Wall-crossing, Hitchin Systems, and the WKB Approximation

S-curves in polynomial external fields

Quadratic differentials and asymptotics of Laguerre polynomials with varying complex parameters

Extremal domains associated with an analytic function I

In this paper we investigate the following two extremal problems: A) Let F be a continuum in the extended complex plane that does not divide and let f(z) be a function analytic on F By D we denote…

Classification of Complete N = 2 Supersymmetric Theories in 4 Dimensions

We define the notion of a complete N = 2 supersymmetric theory in 4 dimensions as a UV complete theory for which all the BPS central charges can be arbitrarily varied as we vary its Coulomb branch…