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Title:
Random groups from generators and relations, and unramified extensions of global fields
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Abstract:
We consider a model of random groups that starts with a free group on n generators and takes the quotient by n random relations, and in particular we study the limiting behavior of this model as n goes to infinity. The abelianization of this model is related to the Cohen-Lenstra heuristics, which predict the distribution of class groups of number fields. We use this model as a jumping off point to develop conjectures on the distribution of the Galois groups of the maximal unramified extensions of varying number fields or function fields (analogous to the fundamental groups of the 3-manifolds in the last talk). We give theorems in the function field case that support these new conjectures. This talk is based on joint work with Yuan Liu and David Zureick-Brown.
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