# Bohemian Matrices and Applications, June 20-22, 2018

Bohemian matrices are matrices with entries drawn from a fixed discrete set of small integers (BOunded HEight Matrix of Integers). Such matrices arise in many applications. For instance, graph incidence matrices have entries from {0, 1} and Bernoulli matrices, which occur in compressed sensing, have entries from {-1, 1}. This workshop aims to investigate existing open questions and applications revolving around such matrices, identify new ones, and plan future activities. The attendees have research expertise drawn from matrix theory, numerical linear algebra, computer algebra, algebraic geometry, number theory, combinatorics, and high performance computing.## Attendees

- Cara Adams, University of Western Ontario
- Pierre Blanchard, University of Manchester
- Eunice Chan, University of Western Ontario
- Rob Corless, University of Western Ontario
- Massimiliano Fasi, University of Manchester
- Nick Higham, University of Manchester
- Lalo Gonzalez-Vega, Universidad de Cantabria
- Ilse Ipsen, North Carolina State University
- Piers Lawrence, EigenPoly Consulting
- Matthew Lettington, Cardiff University
- Theo Mary, University of Manchester
- Vanni Noferini, University of Essex.
- Gian Maria Negri Porzio, University of Manchester
- Juana Sendra, Universidad Politécnica de Madrid
- Steven Thornton, University of Western Ontario
- Françoise Tisseur, University of Manchester

## Schedule

9:10-9:50 Bohemian Matrix Families A specialization in the sense of Pólya, Rob Corless. Video (YouTube).

9:50-10:30 Bohemian Eigenvalues, Steven Thornton. Video (YouTube).

10:30-11:00 Coffee

11:00-11:40 Bohemian Matrices in Numerical Linear Algebra, Nick Higham. Video (YouTube).

11:40-12:30 Discussion

12:30-13:30 Group photo and lunch

13:30-14:00 On Sum-and-Distance Systems, Reversible Square Matrices and Divisor Functions, Matthew Lettington

14:00-15:15 Working

15:15-15:45 Coffee

15:45-16:30 Working

16:30-17:00 Progress Report/Feedback

9:30 -10:30 Working

10:30-11:00 Coffee

11:00-12:30 Working

12:30-13:30 Lunch

13:30-14:00 On the distribution of the number of real eigenvalues of nxn Upper Hessenberg Toeplitz Bohemian matrices when n is fixed, Lalo Gonzalez-Vega

14:00-15:15 Working

15:15-15:45 Coffee

15:45-16:30 Working

16:30-17:00 Progress Report/Feedback

18:30 Workshop reception and dinner, Christie Bistro

*Algebraic Linearizations of Matrix Polynomials*, Eunice Chan

9:30 -10:30 Working

10:30-11:00 Coffee

11:00-12:30 Working

12:30-13:30 Lunch

13:30-16:00 Progress Report/Feedback

## Links

- Bohemian eigenvalues website.
- Bohemian eigenvalues on Steven Thornton's website.
- Workshop group photo.
- Workshop photos.

## Sponsorship

The workshop is sponsored by the Heilbronn Institute for Mathematical Research, the Royal Society and the School of Mathematics at the University of Manchester.