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Friday, October 8, 2021

**Abstract:** The Non Linear Schrödinger Equation (NLS) has been the subject of intense study by the Harmonic Analysis and PDE community. Primarily this is because it is one of the canonical examples of dispersive PDEs that have Soliton solutions. In this talk I will survey results for the discrete analogue of the focusing NLS, and the use of the discrete equation to construct invariant measures. I will conclude with a discussion of Sourav Chatterjee's work on resolving the Soliton resolution conjecture.