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

Wednesday June 20

9:00-9:10 Opening Remarks
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

Thursday June 21

9:00-9:30 Bohemian Matrices: mise en place, Juana Sendra
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

Friday June 22

9:00-9:30 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.

Venue

All talks will take place in Frank Adams Room 1 in the Alan Turing Building of the School of Mathematics at the University of Manchester.The building is 20 minutes walk from the city centre and 15 minutes walk from Piccadilly or Oxford Road train stations; see how to get here.

Other Information

The organizers are Rob Corless and Nick Higham.