Title   name
Harmony of Real and Complex Algebraic Geometry
  Speaker   Rainer Sinn    
  Date 2016-12-09
  Place KAIST
  File  의 1 번째 Real Media 동영상입니다.
Abstract : A matrix completion problem starts with a partially specified matrix, where some entries are known and some are not. We will be interested in completing a partially specified symmetric matrix to a full positive semidefinite matrix. After motivating examples and reviewing the history of the problem we will explain connections to nonnegative polynomials and sums of squares, and a connection to free resolutions. In the second talk we will explain that the classical matrix completion problem coressponds to the case of a coordinate subspace arrangement(square-free monomial ideal). We will then explain that surprisingly matrix completion problem on a variety is related to some properties of its free resolution.