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**public sources and our publisher partners.**The improved microwave tube is a tube such as a klystron wherein bunches of electrons are produced by the input cavity of the tube. These electron bunches are well defined and are produced only when… Continue Reading

We show that the real-valued function S α on the moduli space M 0,n of pointed rational curves, defined as the critical value of the Liouville action functional on a hyperbolic 2-sphere with n ≥ 3… Continue Reading

We compute the number of coverings of $${\mathbb{C}P^1 {\setminus} \{0, 1, {\infty}\}}$$CP1\{0,1,∞} with a given monodromy type over $${\infty}$$∞ and given numbers of preimages of 0 and 1. We show… Continue Reading

A relatively fast algorithm for evaluating Weil-Petersson volumes of moduli spaces of complex algebraic curves is proposed. On the basis of numerical data, a conjectural large genus asymptotics of… Continue Reading

Branched covers of the complex projective line ramified over $0,1$ and $\infty$ (Grothendieck's {\em dessins d'enfant}) of fixed genus and degree are effectively enumerated. More precisely, branched… Continue Reading

We define two tau functions, τ and τ^, on moduli spaces of spectral covers of GL(n) Hitchin systems. Analyzing the properties of τ, we express the rational divisor class of the universal Hitchin’s… Continue Reading

For moduli space of stable parabolic bundles on a compact Riemann surface, we derive an explicit formula for the curvature of its canonical line bundle with respect to Quillen’s metric and interprete… Continue Reading

The tau function on the moduli space of generic holomorphic 1-differentials on complex algebraic curves is interpreted as a section of a line bundle on the projectivized Hodge bundle over the moduli… Continue Reading

A formula for the generating function of the Weil-Petersson volumes of moduli spaces of pointed curves that is identical to the genus expansion of the free energy in two dimensional gravity is… Continue Reading