## Speaker:

Jacob Mayle

## Speaker Link:

## Institution:

University of Illinois, Chicago

## Time:

Thursday, March 11, 2021 - 3:00pm to 4:00pm

## Location:

Zoom: https://uci.zoom.us/j/95528784206

A local-global principle is a result that allows us to deduce global information about an object from local information. A well-known example is the Hasse-Minkowski theorem, which asserts that a quadratic form represents a number if and only if it does so everywhere locally. In this talk, we'll discuss certain local-global principles in arithmetic geometry, highlighting two that are related to elliptic curves, one for torsion and one for isogenies. In contrast to the Hasse-Minkowski theorem, we'll see that these two results exhibit considerable rigidity in the sense that a failure of either of their corresponding everywhere local conditions must be rather significant.