Jan 28
Math/Stats Colloquium: Louis Gaudet, University of Massachusetts Amherst

Title: Extension Problems in Arithmetic Statistics
Abstract: Broadly speaking, arithmetic statistics is the study of enumerating number theoretic objects. Oftentimes there is an infinite set of objects we are interested in (e.g. primes, or quadratic number fields, or elliptic curves, …) and a notion of the size of these objects (e.g., respectively, absolute value, or discriminant, or conductor, …), and we are interested in counting how many of these objects have size less than some bound. I will discuss examples of such questions and introduce some of the techniques used to study them, hoping to convey why I find such questions so compelling. In particular, we will look at enumerative “extension problems” (related to my current work), where we are interested in counting extensions of number fields with a certain Galois group.
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