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

研究非线性偏微分方程组是物理学、经济学、生物学等多个学科提出的大量问题的需要。完全非线性方程是该领域较新的研究课题，但由于与其他领域的联系越来越多，它的重要性也在不断增加。特别地，对Calabi-Yau流形的特殊拉格朗日子流形的研究在弦理论中引起了特别的兴趣，因此也是物理学家和数学家研究的一个活跃领域。由于该领域的迅速发展和广泛的兴趣，它是CBMS地区会议的自然话题。刚接触这一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组中的问题，同时也见证了问题的几何方面如何告知分析方面(反之亦然)的令人惊讶的方式。他作为一名杰出的研究人员和天才的讲解员的声誉使他成为演讲的理想选择。此外，会议产生的专著将引起广泛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.