Abstract: The notion of prescribed generated Jacobian equation was recently introduced by us as a framework to extend the theory of Monge-Ampere type equations in optimal transportation to those in near field geometric optics. In this talk we will present recent work, in collaboration with Feida Jiang, on the classical solvability of the second boundary value problem, which in optics models the illumination of targets with prescribed intensity  by reflection or refraction.

Biosketch: Professor Neil Trudinger is a professor at Australian National University. He is one of the pioneers of nonlinear elliptic equations. Among his most famous achievements are contributions to the Yamabe problem and, together with Xu-Jia Wang, a solution of the Bernstein problem for affine maximal hypersurfaces which had been conjectured by Chern and Calabi. His book "Elliptic partial differential equations of second order", written jointly with David Gilbarg, first published in 1977, is still one of the most popular and cited scientific mathematical monographs. He is a Fellow of the Australian Academy of Science and the Royal Society of London. In 2008 he was awarded Leroy P. Steele Prize for Mathematical Exposition by the American Mathematical Society. He was an invited speaker at the International Congress of Mathematicians in Madrid in 2006.