CAREER Award Program: Alexander Barvinok

这个项目的目的是研究巴拿赫几何中高维现象的应用，如测量集中，优化和算法问题。以下特殊问题将被考虑：混合体积的有效计算，混合判别，非负矩阵的永久，有效的近似计数，以及通过半定规划的近似算法。研究者还将在凸性和优化方面创建新的跨学科课程。美国国家科学基金会强烈鼓励教师作为教育工作者和研究人员的早期发展。教师早期职业发展（Career）计划是一个基金会范围内的计划，为初级教师的整体职业发展提供支持。它在一个项目中结合了对最广泛意义上的高质量研究和教育的支持，以及那些传统上在科学和工程领域代表性不足的人的充分参与。该计划加强并强调了基金会对全面，平衡的学术生涯发展的重要性。

9734138 Barvinok The purpose of this project is to investigate applications of higher-dimensional phenomena in Banach Geometry, such as measure concentration, to optimization and algorithmic problems. The following particular problems will be considered: efficient computation of mixed volumes, mixed discriminants, and permanents of non-negative matrices, efficient approximate counting, and approximation algorithms via semidefinite programming. The investigator will also be creating new interdisciplinary courses in convexity and optimization. The National Science Foundation strongly encourages the early development of academic faculty as both educators and researchers. The Faculty Early Career Development (CAREER) Program is a Foundation-wide program that provides for the support of junior faculty within the context of their overall career development. It combines in a single program the support of quality research and education in the broadest sense and the full participation of those traditionally underrepresented in science and engineering. This program enhances and emphasizes the importance the Foundation places on the development of full, balanced academic careers.