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This note aims to provide an entr\'ee to two developments in two-dimensional topological gravity -- that is, intersection theory on the moduli space of Riemann surfaces -- that have not yet become well-known among physicists.
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M. Douglas, “Strings In Less Than One Dimension and the Generalized KdV Equations,” Phys. Lett. 238B
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E. Witten, “Two-Dimensional Gravity And Intersection Theory On Moduli Space,” Surveys Diff. Geom. 1
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Robbert Dijkgraaf, H. L. Verlinde, and E. P. Verlinde, “Loop Equations and Virasoro Constraints in Nonperturbative 2-D Quantum Gravity,” Nucl. Phys. B348
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P. Di Francesco, P. H. Ginsparg, and J. Zinn-Justin, “2-D Gravity and Random Matrices,” Phys. Rept. 254
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G. McShane, “Simple Geodesics and A Series Constant Over Teichmuller Space,” Invent. Math. 132
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D. Freed, “Two Index Theorems In Odd Dimensions,” Comm. An. Geom. 6
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J. M. Maldacena, G. W. Moore, N. Seiberg and D. Shih, “Exact vs. Semiclassical Target Space of the Minimal String,” JHEP 0410
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M. Aganagic, R. Dijkgraaf, A. Klemm, M. Marino and C. Vafa, “Topological Strings and Integrable Hierarchies,” Commun. Math. Phys. 261
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1991
Cited alongside, same era.
E. Witten, “On Quantum Gauge Theories In Two Dimensions,” Commun. Math. Phys. 141
1991
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J. A. Minahan, “Matrix Models With Boundary Terms and The Generalized Painlevé II Equation,” Phys. Lett. B268
1991
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Z. Yang, “Dynamical Loops in D = 1 D=1 Random Matrix Models,” Phys. Lett. B257
1991
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M. Kontsevich, “Intersection Theory On The Moduli Space Of Curves And The Matrix Airy Function,” Commun. Math. Phys. 147
1992
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S. Dalley, C. V. Johnson, T. R. Morris, and A. Watterstam, Mod. Phys. Lett. A7
1992
Cited alongside, same era.
Y. Itoh and Y. Tanii, “Schwinger-Dyson Equations Of Matrix Models For Open And Closed Strings,” Phys. Lett. B289
1992
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2006
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M. Mirzakhani, “Simple Geodesics and Weil-Petersson Volumes Of Moduli Spaces of Bordered Riemann Surfaces,” Invent. Math. 167
2007
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M. Mirzakhani, “Weil-Petersson Volumes And Intersection Theory On The Moduli Space Of Curves,” Journal of the American Mathematical Society 20
2007
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M. E. Kazarian and S. K. Lando, “An Algebro-Geometric Proof of Witten’s Conjecture,” J. Am. Math. Soc. 20
2007
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B. Eynard and N. Orantin, “Invariants of Algebraic Curves and Topological Expansion,” Comm. in Number Theory and Physics, Vol. 1 (2007), 347–552
2007
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A. Okounkov and R. Pandharipande, “Gromov-Witten Theory, Hurwitz Numbers, and Matrix Models,” Proc. Symp. Pure Math. 80.1
2009
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B. Eynard, “Recursion Between Mumford Volumes of Moduli Spaces,” Ann. Henri Poincaré (2011) 12: 1431
2011
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M. Aganagic, M. C. N. Cheng, R. Dijkgraaf, D. Krefl and C. Vafa, “Quantum Geometry of Refined Topological Strings,” JHEP 1211
2012
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E. Brézin and S. Hikami, “Random Matrix, Singularities, and Open/Closed Intersection Numbers,” Commun. Math. Phys. 02
2013
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E. Witten, “Fermion Path Integrals and Topological Phases,” Rev. Mod. Phys. 88
2016
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