DescriptionThere are a number of interesting problems in physics where one encounters integrals of the form \[ \int dM \, e^{f(M)} g(M) \] where \(M\) are some class of matrices (the set of hermitian matrices, for instance) and \(f(M)\) and \(g(M)\) are functions from matrices to \(\mathbb{R}\). Physical models that reduce to integrals over such spaces of matrices are known as matrix models. These matrix models have a large number applications, ranging from polymer folding (relevant for chemistry or biology) all the way to topological string theory, or quantum gravity. In this project you will learn about matrix models, and describe some of their applications to physics. Pre-requisites and co-requisitesIt is recommended, but not essential, that you should have taken Mathematical Physics II on the second year. If you don't fulfill this pre-requisite but are still interested please talk to us.Reading material
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