Authors: Brantson Yeaman
Mentors: Machiel van Frankenhuijsen
Insitution: Utah Valley University
There has been considerable curiosity at the graduate and postgraduate level in regards to heights, that is, heights in their relation to Diophantine geometry. One application of heights is in the $abc$ conjecture, which remains highly mysterious. Often, the only height undergraduates encounter is the traditional absolute value. This talk seeks to define the height for use in investigating the $abc$ conjecture and connect it at a level that undergraduates with little experience with number theory may approach. It will introduce the idea of a $p$-adic norm of a number, a projective point, and a view that lends itself to both a simple idea of distance, and yet has an analogue in the Hamiltonian numbers.