Random Real Algebraic Geometry

Random Real Algebraic Geometry

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Matthew De Courcy-Ireland, Princeton University
Fine Hall 601

We discuss the work of Fedor Nazarov and Mikhail Sodin on zero sets of randomly generated functions of several real variables. They prove that there is an asymptotic formula for the number of connected components of such a set. The ability to handle functions of more than one variable is a major breakthrough and makes it possible to study many interesting questions. If time allows, we will also explain subsequent work of Peter Sarnak and Igor Wigman. They give universal laws governing more refined topological questions about zero loci of random functions such as how many components have a prescribed topology or how the components are nested inside each other.