NSF/CBMS Regional Conference in the Mathematical Sciences: Fully Nonlinear Equations in Geometry

非线性偏微分方程的研究是来自不同学科的无数问题所必需的：物理学、经济学、生物学等。完全非线性方程是该领域中较新的学科，但由于与其他领域的联系越来越多，它的重要性正在增加。特别是，对Calabi-Yau流形的特殊拉格朗日子流形的研究在弦理论中是一个特别有趣的研究领域，因此在物理学家和数学家中都是一个活跃的研究领域。由于该领域的快速发展和广泛关注，这是建立信任管理机制区域会议的自然议题。刚进入该领域的研究人员和研究生可以看到当前感兴趣的几何问题如何被重新表述为非线性偏微分方程中的问题，同时也可以看到问题的几何方面经常以令人惊讶的方式通知分析方面（反之亦然）。这次会议的首席讲师尼尔·特鲁丁格（Neil Trudinger）教授也增加了会议的吸引力。他作为一位杰出的研究者和有天赋的讲解家的名声使他成为演讲的理想人选。此外，会议产生的专著将引起许多领域的科学家的兴趣。

The study of nonlinear partial differential equations is necessitated by countless problemsfrom diverse disciplines: physics, economics, biology, etc. Fully nonlinear equations is a more recent subject within this field, but its importance is increasing due to the growing number of connections to other fields. In particular, the study of special Lagrangian submanifolds of Calabi-Yau manifolds is of particular interest in string theory, and consequently an active area of research among physicists and mathematicians alike.Because of the rapid growth and broad interest of the field, it is a natural topic for a CBMS Regional Conference. Researchers and graduate students who are new to the field can see how geometric problems of current interest can be reformulated as problems in nonlinear PDE, and at the same time witness the often surprising ways in which the geometric aspects of the problem inform the analytic aspects (and vice versa).Adding to the appeal of the meeting is the principal lecturer, Prof. Neil Trudinger. His reputation as an eminent researcher and gifted expositor make him an ideal choice to deliver the lectures. Moreover, the monograph resulting from the meeting will be of interest to scientists in a wide range of fields.