In this talk we shall derive Tutte's Recursion from 1 marked boundary planar maps. We shall then obtain the Schwinger-Dyson Equations (SDEs) and give a matrix model proof of Tutte's Recursion, and time permitting, we will study higher genus Tutt's Recursions.

In this talk I will give a brief introduction to random matrix theory and Dirac ensembles. We will discuss their spectral statistics, relationship to random matrix ensembles, and the use of a procedure known as "Topological Recursion".

Abstract: In this talk, we will explain recent finiteness results in the theory of linear symbolic dynamics. These results allow us to reformulate in the language of symbolic dynamics the very old classification problem of all groups whose group rings are Noetherian. If time permits, we will also mention another application on the shadowing property of linear cellular automata.