Fall 2021

The seminar meets Wednesdays at 2pm, in Jones 302. Email the organizer for information or to be added to the mailing list.

Next talk (9/29)

Cordelia Li

Copositive Matrices, their Dual, and the Recognition Problem

Abstract: Copositivity is a generalization of positive semidefiniteness. It has applications in economics, operations research, and statistics. An $n$-by-$n$ real matrix $A$ is copositive (CoP) if $x^TAx \ge 0$ for any nonnegative vector $x \ge 0$. The CoP matrices form a proper cone. A CoP matrix is ordinary if it can be written as the sum of a positive semidefinite (PSD) matrix and a symmetric nonnegative (sN) matrix. When $n < 5$, all copositive matrices are ordinary. However, recognition that a given CoP matrix is ordinary and the determination of an ordinary decomposition is an unresolved issue. Here, we make observations about CoP-preserving operations, make progress about the recognition problem, and discuss the relationship between the recognition problem and the PSD completion problem. We also mention the problem of copositive spectra and its relation to the symmetric nonnegative inverse eigenvalue problem.

10/06Gabriel Martins (Sacramento State)Title TBA
9/29Cordelia Li'22Copositive matrices, their dual, and the Recognition Problem
9/22Merielyn Sher'22Enumerating minimum path covers of trees
9/15Bjoern Muetzel (Eckerd College)Harmonic forms on pinched surfaces (Slides)
9/08Gexin YuSufficient conditions for 2-dimensional graph rigidity