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Daniel Kim Geometry in the non-archimedean world, April 9, 2019

Daniel will give the math table talk next Tuesday (April 9nd). His title and abstract are below.
Title: Geometry in the non-archimedean world
Abstract. In number theory, there are numbers called p-adic numbers that are treated on an equal footing as the real numbers. We have some idea of how to do geometry over the real numbers; we learn about manifolds and stuff. But how do we do geometry over the p-adic numbers? In this talk, I will try to explain why p-adic numbers naturally arise in studying numbers. These numbers satisfy a certain non-archimedean property, and geometry becomes horribly non-intuitive due to this. I will talk about how people developed different notions of geometry to overcome this. We will also see why number theorists visualize p-adic numbers as a fractal-like tree figure.