Letters in Mathematical Physics

, Volume 105, Issue 10, pp 1427–1448 | Cite as

Equivalence of the Open KdV and the Open Virasoro Equations for the Moduli Space of Riemann Surfaces with Boundary

  • Alexandr Buryak


In a recent paper, Pandharipande, Solomon and Tessler initiated a study of the intersection theory on the moduli space of Riemann surfaces with boundary. The authors conjectured KdV and Virasoro type equations that completely determine all intersection numbers. In this paper, we study these equations in detail. In particular, we prove that the KdV and the Virasoro type equations for the intersection numbers on the moduli space of Riemann surfaces with boundary are equivalent.


Riemann surfaces with boundary moduli space KdV equations 

Mathematics Subject Classification

Primary 35Q53 Secondary 14H10 


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of MathematicsETH ZurichZurichSwitzerland

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