Number Theory Informed by Computation

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Number Theory Informed by Computation is written by Jennifer S. Balakrishnan and published by . It's available with International Standard Book Number or ISBN identification 1470461242 (ISBN 10) and 9781470461249 (ISBN 13).

This book is a collection of lecture notes from the Graduate Summer School "Number Theory Informed by Computation" held at the IAS/Park City Mathematics Institute 2022. The lectures address topics at the interface between number theory and computation, both terms interpreted broadly. Included are lectures on polynomial-time algorithms for problems in algebraic number theory, algorithms for counting points on mod $p$ reduction of a variety working with many values of $p$ simultaneously, arithmetic statistics, the theory of lattices, Brauer-Manin obstruction, the theory of rigid cocycles, and the inverse Galois problem. The volume starts with the notes of Hendrik Lenstra's public lecture, aimed at a general audience, where the speaker explains how modern abstract algebra can be used to explain concrete properties of integers. This volume is aimed at students with a background in graduate level number theory. For some expositions, undergraduate abstract algebra may be sufficient, while others might require basic algebraic geometry.