Location: RI 208
Speaker: Shaun Fallat, University of Regina
Title: Recent Advances on Inverse Spectral Problems for Graphs: 'Strong’ Matrix Properties
Abstract:
The inverse eigenvalue problem (IEP-G) for a graph \(G\) asks to determine if a given multiset of real number \(\Lambda\) is the spectrum of a real symmetric matrix \(A\) that fits \(G\) This important and largely unresolved question has been referred to as “finding a needle in a haystack” Recently developed tools (i.e., strong matrix properties) have opened some new directions by providing matrix theoretic and combinatorial criterion for the existence of a “nice” matrix (or needle) that guarantees the existence of another matrix in a “nearby” haystack! This talk will focus on and survey several different strong matrix properties (SAP,SMP, SSP, SIPP, SNIP, SSVP, nSSP,…) and illustrate some interesting implications to the IEP-G.