A Bohemian is a BOunded HEight Matrix of Inte gers (BOHEMI\, close enough). Recently I have bec ome very interested in such things\; see bohemianm atrices.com for some reasons why. In this hour we will look at a collection of Maple procedures des igned (this month!) to answer questions about comp lex symmetric\, tridiagonal\, irreducible\, zero-d iagonal Bohemians (a new class\, chosen just for t his workshop). This means that there will be (#P) ^(m-1) m-dimensional such matrices for a given pop ulation of elements P\, which for this class canno t contain zero. We will look at fast ways to gene rate these matrices\, how to generate fast(ish) co de to compute the characteristic polynomials (and why)\, and generally use this topic as an excuse t o learn some Maple programming.

The hour will assume some familiarity with programming\; fo r instance\, if you know Matlab\, then you very ne arly know Maple already (in some ways they are sim ilar enough that it causes confusion\, unfortunate ly). But it will not be necessary\; I hope to enc ourage a friendly atmosphere and we'\;ll genera te some interesting (I hope) images\, and perhaps some interesting mathematical conjectures. But ev en if you know Maple well\, you might learn someth ing interesting. All the scripts/worksheets/workb ooks have been made available at http://publish.uw o.ca/~rcorless/Maple2019/ so you may download them and run and modify the examples yourself\, and ge nerate your own Bohemian images.

Indeed I believe that it is entirely likely that you will be able to formulate your own Bohemian conjectures during this activity\; and it has been known for participants to prove theorems about them\, during the lecture. Who knows\, perhaps your next paper will get its main result during this activity.

Licences for Maple valid for one month have been generously provided for participants by Mapl esoft. There will be a representative from Mapleso ft here to answer any questions. LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR