Clemens Bruschek (University of Vienna)
Algebraic Geometry
Abstract:
Algebraic geometry is the study of geometrical objects given by algebraic data. For example one is interested in the structure of the set of solutions of a finite set of polynomial equations in several variables over a field. After a quick introduction to the very basics of algebraic geometry we will focus on the study of such solutions in the ring of formal or convergent power series. This will lead to the study of infinite dimensional algebraic varieties, so called "arc spaces" and their natural generalizations. Along this roadmap we will point out to other research topics the field.
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