Audie Warren

Affine group energy

In this talk we present new results on energy bounds in the affine group. This leads to new results concerning growth of sets of lines in the plane under composition, and has applications in an incidence theorem of Rudnev and Shkredov, leading to a further result relating to Ungar's Theorem, and a new super-quadratic expander. This is joint work with Petridis, Roche-Newton, and Rudnev.