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Junior GST
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Charlie Reid, RLM 9.166: Witten's Two Dimensional Gravity Conjecture
Monday, March 11, 2019, 12:00pm - 01:00pm
In a theory of quantum gravity one must integrate over all metricsone could put on spacetime. This is a very difficult idea toflesh out in general, but in two dimensions there are a few reasonableapproaches. In 1991, Ed Witten conjectured a correspondencebetween two of these approaches: "topological gravity" whichis intersection theory on moduli spaces of Riemann surfaces (GromovWitten theory of the point), and the "one matrix model" whichcounts ways of cutting a surface into polygons. Dual graphs ofpartitions of surfaces into polygons are the Feynman diagramsfor certain integrals on the space of hermitian matrices, thusthe name "matrix model". The matrix model is then governed bythe KdV equation. Witten conjectured (and Kontsevich later proved)that intersection numbers on moduli space are similarly governedby the KdV equation. I will describe these two theories of 2Dquantum gravity as much as I can, and give a precise statementof the Witten Conjecture.
Location: RLM 9.166

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