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In recent works, [20],[21], descendent integrals on the moduli space of Riemann surfaces with boundary were defined.
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2015
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by same author, Equivalence of the open KdV and the open Virasoro equations for the moduli space of Riemann surfaces with boundary , Letters in Mathematical Physics (2015), 1–22, doi:10.1007/s11005-015-0789-3
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B. Safnuk, Combinatorial models for moduli spaces of open Riemann surfaces , arXiv:1609.07226, 2016
2016
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by same author, Topological recursion for open intersection numbers , arXiv:1601.04049, 2016
2016
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A. Alexandrov, A. Buryak, and R. J. Tessler, Refined open intersection numbers and the Kontsevich-Penner matrix model , Journal of High Energy Physics 2017:123
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2006
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D. Cimasoni and N. Reshetikhin, Dimers on surface graphs and spin structures. I , Comm. Math. Phys. 275
2007
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M. Mirzakhani, Weil-Petersson volumes and intersection theory on the moduli space of curves , J. Amer. Math. Soc. 20
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A. Okounkov and R. Pandharipande, Gromov-Witten theory, Hurwitz numbers, and matrix models , Algebraic geometry—Seattle 2005. Part 1, Proc. Sympos. Pure Math., vol. 80, Amer. Math. Soc., Providence, RI, 2009, pp. 325–414
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2011
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2011
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2012
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2014
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2017
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A. Buryak and R. J. Tessler, Matrix models and a proof of the open analog of Witten’s conjecture , Communications in Mathematical Physics 353
2017
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2017
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by same author, Moduli of Open Stable Maps to a Homogeneous Space , arXiv:1709.07402, 2017
2017
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A. Bawane, H. Muraki, and C. Rim, Open KdV hierarchy and minimal gravity on disk , Physics Letters B 783
2018
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2018
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R. Dijkgraaf and E. Witten, Developments in Topological Gravity , 2018, arXiv:1804.03275
2018
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by same author, Open r r -spin theory I: Foundations , International Mathematics Research Notices (2021), doi:10.1093/imrn/rnaa345
2021
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