The nonlinear Schrodinger equation (NLS) appears in a wide range of physical phenomena. For example, it is a leading order approximation of the slowly varying envelope of waves in optics, and it also the mean field limit in many-body quantum systems.
In this talk, we focus solely on the mathematical analysis of NLS, and discuss what it means to solve the equation, and how using simple Calculus, we can establish a formation of a singularity in finite time.
The nonlinear Schrodinger equation: wellposedness and blowup
Abstract: Deep neural networks are a centerpiece of modern machine learning. They are also fascinating mathematical objects, about which much remains unclear. In this talk I will define neural networks, explain how they are used in practice, and give a survey of the big theoretical questions they have raised. If time permits, I will also explain how neural networks are related to a variety of classical questions in mathematics, ranging from random matrix theory, to optimal transport, and combinatorics of hyperplane arrangements.