Todor Milanov: Matrix model for the total descendent potential of a simple singularity of type D

Abstract: I am planning to talk about my recent paper, joint with Alexander Alexandrov, with the same title. It was conjectured by Witten that the intersection theory on the moduli space of curves is governed by the KdV hierarchy. The conjecture was first proved by Kontsevich. He was able to express the intersection numbers in terms of the asymptotic expansion of a certain Hermitian matrix integral and to prove that the asymptotic expansion coincides with a tau-function of KdV given in the so-called Miwa parametrization. We were able to construct a Hermitian matrix integral whose asymptotic expansion coincides with the Miwa parametrization of the total descendent potential of a simple singularity of type D. Recalling a LG/LG mirror symmetry result of Fan--Jarvis--Ruan, we can also conclude that the asymptotic expansion of our integral gives the FJRW-invariants of the Berglund--Hubsch dual singularity D^T.