CAREER Award Program: Alexander Barvinok

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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.