Georgia Institute of Technology College of Sciences

This talk is intended to be a cocktail of many things. I will start with standard random matrices (called GUE in the slang) and formal computations which leads one to the main problem of counting planar diagrams. This was done by physicists, though the main computation of generating functions for such planar diagrams go through an analytic tools. Here I will change the topic to analysis, and get through with the help of Chebyshev polynomials and how these can be used to solve a minimization problem and then from there to compute several generating functions of planar diagrams. Then I will talk about tridiagonalization which is a main tool in matrix analysis and point out an interesting potential view on this subject.