3.1 Algorithms in algebraic number theory| Hendrik Lenstra, Universiteit Leiden
Channel: IAS | Park City Mathematics Institute | PCMI
Date: 28/07/2022

This minicourse is about algorithms for computational problems that one encounters in algebraic number theory. The emphasis is not on actual computations, but on issues of mathematical interest that arise in the design of efficient algorithms; here "efficient" is generally taken to mean "polynomial-time". We shall discuss problems for which such algorithms are known, and techniques for circumventing problems for which no efficient algorithms are known. Special attention will be given to the computation of rings of integers, and to the computation of power residue symbols and Artin symbols.

Suggested reading: Daan van Gent, Polynomial-time algorithms in algebraic number theory. These are the course notes of preparatory lectures that were presented in July, 2021. They can be found at https://pub.math.leidenuniv.nl/~gentdmhvan/pdf/pcmi.pdf

IAS | PCMI Graduate Summer Session
https://www.ias.edu/pcmi/2022-graduate-summer-school-course-descriptions