(I) Combinatorial and matrix models for moduli space of curves


You-Cheng Chou
2016-10-24  15:30 - 17:00
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.)

In these two talks a complete proof of Witten\'s conjecture on the structure of descendent potential of moduli space of stable curves will be given. In the first talk the background material will be prepared. Especially the combinatorial model of moduli spaces of curves will be discussed in details. Based on it the potential can be rewritten in terms of matrix integrals. In the second talk we show that the potential is annihilated by the Virasoro operators by way of the KdV equations. We follow the original 1992 proof by Kontsevich closely. References: [1] Arbarello, Cornalba, Griffiths: Geometry of Algebraic Curves. vol 2 [2] Lando-Zvonkin, Graphs on Surfaces and Their Applications