Moscow Mathematical Journal
Volume 16, Issue 1, January–March 2016 pp. 27–44.
Open Intersection Numbers and the Wave Function of the KdV Hierarchy
Recently R. Pandharipande, J. Solomon and R. Tessler initiated a study of the intersection theory on the moduli space of Riemann
surfaces with boundary. They conjectured that the generating series of
the intersection numbers is a specific solution of a system of PDEs, which
they called the open KdV equations. In this paper we show that the
open KdV equations are closely related to the equations for the wave
function of the KdV hierarchy. This allows us to give an explicit formula for the specific solution in terms of Witten’s generating series of
the intersection numbers on the moduli space of stable curves. 2010 Math. Subj. Class. Primary: 35Q53; Secondary: 14H10.
Authors:
A. Buryak
Author institution: Department of Mathematics, ETH Zurich, Ramistrasse 101 8092, HG G 27.1, Zurich, Switzerland
Summary:
Keywords: Riemann surfaces with boundary, moduli space, KdV equations.
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