Title: Towards a sharp restriction inequality for the circle
Abstract: We discuss joint work with Emanuel Carneiro, Damiano Foschi, and Diogo Oliveira e Silva, providing progress towards the sharp constant for the $L^2$ to $L^6$ Fourier extension inequality for the circle. Following Foschi's method for the analogous problem for the three sphere, the problem is decomposed into a sharp bilinear and a sharp trilinear inequality, of which we prove the sharp trilinear inequality. The proof uses fine estimates for integrals of products of Bessel functions.