A 2008 general overview on Weil-Petersson geometry is offered. A preliminary plan for the subsequent CBMS lectures at Central Connecticut State University is included. Mirzakhani's solution of Witten-Kontsevich is not included - this work essentially requires its own lectures. Lectures on Mirzakhani's Witten-Kontsevich…
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7 results for “Witten-Kontsevich”
Novel approach for large genus intersection number asymptotics.
problem Computing intersection numbers in large genus.
method Resurgent analysis of n-point functions with quantum curve.
result Extension of Aggarwal's results and new -spin and Theta-class intersection numbers.
Completed volumes match with combinatorial classes of the double ramification cycle.
problem Computing Masur-Veech volumes for quadratic differentials.
method Describing components of the double ramification cycle and their excess intersection classes, leading to a recursion for completed volumes.
result Completed volumes agree with top intersection of tautological classes on the double ramification cycle.
The materials accompany a lecture short course presented at the 2011 Park City Mathematics Institute, Graduate Summer School on Moduli Spaces of Riemann Surfaces. The lectures were part of/coordinated with an overall program, including lectures by Ursula Hamenstadt on Teichmueller Theory, Andy Putman on Mapping Class a…
Counting meanders on surfaces of arbitrary genus, with precise asymptotics.
problem Counting and understanding meanders on surfaces of arbitrary genus.
method Square-tiled surfaces, moduli spaces of Abelian and quadratic differentials, Witten-Kontsevich 2-correlators.
result Asymptotic probability and polynomial growth of meanders with intersections.
Formula for volumes of odd strata of quadratic differentials using graph intersection numbers.
problem Calculating volumes of specific strata of quadratic differentials.
method Expressed volumes as a sum over stable graphs, with coefficients as intersection numbers of psi classes with combinatorial classes.
result Formula for volumes of odd strata of quadratic differentials.
Counting lattice points in moduli space of Klein surfaces.
problem Count lattice points in moduli space of Klein surfaces.
method Introduced metric Möbius graphs, counted lattice points weighted by non-orientability measure, deduced recursion for volumes.
result Proved refined version of Norbury's recursion and computed refined Euler characteristic.