We show that the real-valued function SÎ± on the moduli space M0,n of pointed rational curves, defined as the critical value of the Liouville action functional on a hyperbolic 2-sphere with n â‰¥ 3â€¦ (More)

Two types of connected chord diagrams with chord endpoints lying in a collection of ordered and oriented real segments are considered here: the real segments may contain additional bivalent verticesâ€¦ (More)

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 Quillenâ€™s metric and interpreteâ€¦ (More)

A relatively fast algorithm for evaluatingWeil-Petersson volumes of moduli spaces of complex algebraic curves is proposed. On the basis of numerical data, a conjectural large genus asymptotics of theâ€¦ (More)

The isomonodromic tau function of the Fuchsian differential equations associated to Frobenius structures on Hurwitz spaces can be viewed as a section of a line bundle on the space of admissibleâ€¦ (More)

We explicitly compute the diverging factor in the large genus asymptotics of the Weil-Petersson volumes of the moduli spaces of n-pointed complex algebraic curves. Modulo a universal multiplicativeâ€¦ (More)

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 Quillenâ€™s metric and interpretâ€¦ (More)

The cycle graph introduced by Bafna and Pevzner is an important tool for evaluating the distance between two genomes, that is, the minimal number of rearrangements needed to transform one genome intoâ€¦ (More)

The aim of this note is to prove a rather explicit formula for the generating function of the Weil-Petersson volumes of the moduli spaces Mg,n of smooth npointed curves of genus g that wasâ€¦ (More)

We propose a universal approach to a range of enumeration problems in graphs. The key point is in contracting suitably chosen symmetric tensors placed at the vertices of a graph along the edges. Inâ€¦ (More)