题目：The Affine Bernstein Problem

报告人：汪铃（Bocconi university）

时间：2026年11月19日（星期四）15:00-16:00

地点：文北楼102教室

摘要：

The affine Bernstein problem asks whether every locally uniformly convex affine maximal graph that is complete with respect to the induced Euclidean metric must be an elliptic paraboloid. As an affine analogue of the classical Bernstein problem, it has a rich history, with fundamental contributions by Trudinger and Wang. Recent work by OpenAI, building on the framework developed by Trudinger and Wang, establishes Bernstein rigidity in dimensions three through nine. Together with the existence of smooth nonquadratic examples in dimension ten, this identifies the sharp dimension threshold. The aim of this talk is to provide an overview of the problem and the ideas behind these developments. I will first explain the Trudinger–Wang framework, then outline how OpenAI builds on it to establish the higher-dimensional rigidity result. If time permits, I will discuss some of the key steps of OpenAI's proof in details.