Semi-algebraic geometry

Laura Phillips

Frank Adams 1,

When one starts to do algebraic geometry over the real field, the presence of the order means that the semi-algebraic sets quickly emerge as natural objects of study. In this talk I'll introduce semi-algebraic sets and functions, and describe some of their nice properties. The real valued continuous, semi-algebraic functions on the real line â€‹form a ring. Using this ring as an example, I'll introduce the real spectrum of a commutative ring - one of the spectral spaces of last week's talk. If there's time I'll talk a little bit about the model theory of real closed fields, and try to indicate why there have been so many useful interactions between model theory and real algebraic geometry.

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