Field Patching and Algebraic Structures

Explore the intricacies of field patching and algebraic structures in this 43-minute AMS Invited Address delivered at the 2022 Virtual Joint Mathematics Meetings. Delve into topics such as number fields, U invariant, and the local to global principle as presented by Daniel Krashen from the University of Pennsylvania. Gain insights into the classical approach, the developments of the late 90s, and the application of field patching to algebraic groups. Discover how these concepts contribute to understanding general algebraic structures and their significance in modern mathematics.

Intro
Algebraic structures
Number fields
U invariant
Question
Answer
Why Care
Classical Approach
Does this even help
The late 90s
Field patching
Algebraic groups
Local to global principle
General algebraic structures