“数理论坛”第100期：Geometry in Solving Systems of Quadratic Equations

报告题目

Geometry in Solving Systems of Quadratic Equations

报告时间

2019.6.18 16:30-18:00

报告地点

东区综合楼A座701会议室

报告人

蔡剑锋（香港科技大学数学系）

报告人

简介

• Associate Professor, Department of Mathematics, Hong Kong University of Science and Technology, 2015--

• Assistant Professor,Department of Mathematics,University of Iowa, 2011--2015.

• CAM Assistant Adjunct Professor,Department of Mathematics,University of California, Los Angeles, 2009--2011.

• Ph.D. in Mathematics,Chinese University of Hong Kong, 2004--2007.

• M.Sc. in Computational Mathematics, Fudan University, 2001--2004.

• B.Sc. in Computational Mathematics,Fudan University,1996--2000.

报告摘要

Systems of quadratic equations arise from many fundamental problems in data science and imaging. As an example, we consider the problem of solving systems of phaseless equations |<a_i,x>|^2=y_i, i=1,…,m and x in R^n is unknown. One application of great importance is the phase retrieval problem, which provides promising and indispensable tools in a wide spectrum of techniques including X-ray crystallography, diffraction imaging, microscopy, and even quantum mechanics. We will present two results related to geometry in solving systems of phaseless equations. One is to use Riemannian optimization and the other is to analyze the geometric landscape of a non-convex optimization for solving phaseless equations. Both results need number of equations is only proportional to the number of unknowns, under a Gaussian random model. Similar geometric results for other systems of quadratic equations were provided by us or other authors under various settings.

邀请人

向东进 教授

2019年6月12日