1/3 Around the inverse Galois problem, Olivier Wittenberg, Institut Galilée-Univ Sorbonne Paris Nord
Channel: IAS | Park City Mathematics Institute | PCMI
Date: 2022-08-03

Lecture part 1/3 Olivier Wittenberg, Institut Galilée – Université Sorbonne Paris Nord. Title: Around the inverse Galois problem

The inverse Galois problem asks whether any finite group can be realised as the Galois group of a Galois extension of the rationals. This problem and its refinements have stimulated a large amount of research in number theory and algebraic geometry in the past century, ranging from Noether's problem (letting X denote the quotient of the affine space by a finite group acting linearly, when is X rational?) to the rigidity method (if X is not rational, does it at least contain interesting rational curves?) and to the arithmetic of unirational varieties (if all else fails, does X at least contain interesting rational points?). The goal of the lecture series will be to provide an introduction to these topics.

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