# Localization and unique continuation on the integer lattice, I

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Abstract: This will be a series of technical lectures on my recent work with Jian Ding. After a brief review of the mathematics of Anderson localization, I will explain our unique continuation result. To motivate our proof, I will describe the unique continuation result of Buhovski--Logunov--Malinnikova--Sodin for harmonic functions on the integer lattice. I will then explain how to modify this argument, introducing tools from probability theory, to obtain a unique continuation result for Schrodinger operators on the lattice with random potentials.