The "Witten-Kontsevich intersection numbers" are scattering amplitudes in the context of the most simplified possible model of quantum gravity and string theory: a very low-energy quantum gravity, simplified to the extreme to keep only the fundamental phenomenon of topology fluctuations.
These are positive integer or rational numbers, and they are the basis of all the more complex string theories, and of all surface enumerative geometry, in particular in algebraic geometry. Moreover, the conjecture of E. Witten, whose proof gave the Fields Medal to M. Kontsevich, indicates that these same numbers are relevant in almost all problems of mathematical physics: random matrices, statistical physics on a random surface, wave propagation in a canal, or the semi-classical approximation of the solutions of Schrödinger equations, and of all field theories in quantum physics. In particular, they play an important role in the black-hole model developed by Jackiw-Teitelboim.
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