The Bernstein problem asks whether entire minimal graphs in dimension N + 1 are necessarily hyperplanes. This problem was solved in combined works of Bernstein, Fleming, De Giorgi, Almgren, and Simons ("yes" if N < 8), and Bombieri-De Giorgi-Giusti ("no" otherwise). We will discuss the analogue of this problem for minimizers of general parametric elliptic functionals. In particular, we will discuss new examples of nonlinear entire graphical minimizers in dimension N = 6, and recent joint work with Y. Yang towards constructing such examples in the lowest possible dimension N = 4.

Bio: Professor Mooney received his Ph.D. at Columbia University in 2015. He was an NSF Postdoctoral Research Fellow at UT Austin from 2015-16, and a Postdoctoral Researcher at ETH Zurich from 2016-18. Since 2018, he has been an Assistant Professor at UC Irvine.