Title: Preserving positivity for rank-constrained matrices
Speaker: Prof Apoorva Khare Stanford university
Date: 28 November 2013
Time: 3:30 - 4:30 p.m.
Venue: Lecture Hall I, Department of Mathematics
We study the problem of characterizing functions, which when applied entrywise, preserve Loewner positivity on distinguished submanifolds of the cone of positive semidefinite matrices. Following the work of Schoenberg and Rudin (and several others), it is well-known that entrywise functions preserving positivity in all dimensions are necessarily absolutely monotonic. However, there are strong theoretical and practical motivations to study functions preserving positivity in a fixed dimension $n$. Such characterizations are known only in the $n=2$ case.