From noncommutative field theory towards topological recurrence.

Abstract:

Finite-dimensional approximations of noncommutative quantum field theories are matrix models. They often show rich mathematical structures: many of them are exactly solvable or even related to integrability, or they generate numbers of interest in enumerative or algebraic geometry. For many matrix models, it was possible to prove that they are governed by a universal combinatorial structure called Topological Recursion. The probably most beautiful example is Kontsevich's matrix Airy function which computes intersection numbers on the moduli space of stable complex curves. The Kontsevich model arises from a $\lambda\Phi^3$-model on noncommutative geometry. The talk addresses the question which structures are produced when replacing $\lambda\Phi^3$ by $\lambda\Phi^4$. The final answer will be that $\lambda \Phi^4$ obeys an extension of topological recursion. We encounter numerous surprising identities on the way.

mathematical physics

Audience: researchers in the topic

Noncommutative Geometry and Physics

Series comments: Noncommutative geometry is a very general mathematical paradigm arising from quantum mechanics. As such, it permeates different branches of mathematics and physics.

The series of monthly talks accompanies the special issue of Journal of Physics A and is intended to present the many facets of the emergence of noncommutativity in physics.

Past seminars can be viewed on YouTube channel.