# MS-12 The Nonnegative Inverse Eigenvalue Problem (Nonnegative Inverse Eigenvalue)

### Organizers: Charles R. Johnson (The College of William and Mary) and Pietro Paparella (University of Washington Bothell)

The longstanding nonnegative inverse eigenvalue problem (NIEP) is to characterize the spectra of (entrywise) nonnegative matrices. The NIEP is unsolved when order greater than five and remains one of the premier unsolved problem in matrix analysis. The real NIEP and symmetric NIEP are important variants that are also unsolved for orders greater than five. The NIEP has been open since 1949 and has drawn the attention of numerous researchers from many distinct areas of mathematics. The purpose of this CMS is to bring together various international researchers working on the NIEP and its variants in order to disseminate recent advances and connections to other branches of mathematics. We also welcome talks on the single-eigenvalue NIEP (stochastic/doubly stochastic regions).

### Speakers

**Sasmita Barik**, *On the spectra of multi-directed bipartite graphs*

**Raphael Loewy**, *A new necessary condition for the spectrum of nonnegative symmetric 5×5 matrices*

**Carlos Marijuán**, *On Symmetric Nonnegative Realizability*

**Pietro Paparella**, *A matricial view of the Karpelevič Theorem*

**Miriam Pisonero**, *5-Spectra of Symmetric Nonnegative Matrices*

**Ricardo Soto**, *Structured nonnegative inverse elementary divisors problem*

**Elvis Valero**, *A recursive condition for "The symmetric nonnegative inverse eigenvalue problem"*