【报告摘要】 Low-rank matrix completion is an interdisciplinary problem in which one seeks to complete a rank-r matrix X, by only observing a subset of its entries at specified locations. Such an observation is tantamount to subjecting an element X from the classical determinantal variety to a coordinate projection. This talk will be concerned with the problem of characterizing the coordinate projections that have zero-dimensional generic fiber, or equivalently, of characterizing the observation patterns that are generically finitely completable at rank r. The talk will review basic connections with Groebner bases and matroid theory, as well as discuss recent developments connecting the problem to local coordinates on Grassmannians.

【报告人简介】 Manolis C. Tsakiris holds a PhD in Mathematics from the University of Genova advised by Aldo Conca, and a PhD in Electrical Engineering from Johns Hopkins University advised by Rene Vidal. His research interests lie in commutative algebra and the applications of algebraic geometry to data science. He is currently an Associate Professor at the Academy of Mathematics and Systems Science, in the Chinese Academy of Sciences, in Beijing. ?