Kevin Hughes

Square function estimates for planar curves over local fields

I will talk about recent work with Kirsti Biggs and Julia Brandes on square functions for planar curves over local fields. I will start the talk by describing what square functions are and by motivating their study in number theory and analysis. From there, I will state our main result, indicate some of the difficulties compared to previous works, and finally prove it using some fun, yet simple, blend of analysis and algebraic geometry.