Growth, Incidence Bounds and Affine Group Energy

Oliver Roche-Newton

Radon Institute for Computational and Applied Math, Linz, Austria

Date and time: 6pm, Tuesday, September 10, 2019

Place: Courant Institute, WWH1314

Incidence Geometry, and in particular the Szemer├ędi-Trotter Theorem, has a long history of applications to sum-product type results. This talk will discuss how viewing lines as elements of the affine group and studying their energy can lead to improved incidence bounds in certain (asymmetric) settings, and how these new incidence bounds can be applied to prove new results in sum-product theory.