Finite-dimensional approximations of noncommutati ve quantum field\ntheories are matrix models. They often show rich mathema tical\nstructures: many of them are exactly solvable or even related to\ni ntegrability\, or they generate numbers of interest in enumerative or\nalg ebraic geometry. For many matrix models\, it was possible to prove that\n they are governed by a universal combinatorial structure called\nTopologi cal Recursion. The probably most beautiful example is\nKontsevich's matrix Airy function which computes intersection numbers on\nthe moduli space of stable complex curves. The Kontsevich model arises\nfrom a $\\lambda\\Phi ^3$-model on noncommutative geometry. The talk\naddresses the question whi ch structures are produced when replacing\n$\\lambda\\Phi^3$ by $\\lambda\ \Phi^4$. The final answer will be that\n$\\lambda \\Phi^4$ obeys an extens ion of topological recursion. We\nencounter numerous surprising identities on the way.
\n LOCATION:https://researchseminars.org/talk/NCGandPH/5/ END:VEVENT END:VCALENDAR