In their recently published book, Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks, Persi Diaconis and Ron Graham – both mathematicians and a professional magician and juggler, respectively – reveal the “secrets of amazing, fun-to-perform card tricks – and the profound mathematical ideas behind them.” At BIRS, we particularly like the chapter, Is this Stuff Actually Good for Anything, which tackles the subject of Bruijn sequences, in which the authors include a section that provides a glowing review of the BIRS workshop, Generalizations of de Bruijn Cycles and Gray Codes, held in December of 2004.

The BIRS workshop was quite likely the first meeting of its kind to focus on the theory, constructions and generalizations of de Bruijn cycles, despite the fact that many people in diverse areas have been working on aspects of universal cycles of one kind or another for quite some time. Its intent was to give an overview of the various known results on de Bruijn sequences and universal cycles in general, and to exploit the diversity of the attendees in order to stimulate new work, focussing on several questions in which progress seems imminent or likely. According to Diaconis and Graham, BIRS provided an ideal setting for such interactions.

In their article, they describe how 25 researchers, including the likes of Brendan McKay (Australian National University), Eduardo Moreno (Universidad Adolfo Ibañez, Chile), Robert Johnson (Queen Mary University of London) and international experts including Hal Fredricksen (Naval Postgraduate School) who has over 40 years of experience in the field, Frank Ruskey (University of Victoria) who “has the world’s best programs for generating all kinds of de Bruijn sequences and Gray codes on his Web site” and Carla Savage (North Carolina State University), an expert on nonstandard constructions, came together in the “exotic location” of Banff, Alberta.

They go on to state how:

“There were really friendly introductory and expository talks aimed at bringing newcomers up to speed and making sure we were all on the same page. There were announcements of new results, big and small…Much time was spent in small groups where people go over special cases slowly and ask each other “silly questions” that might be embarrassing if asked in a large group.”

They also describe “one of the most spectacular new results [which] was Robert Johnson’s solution of the notorious ‘middle-layer’ problem” and how this particular problem relates to the magic behind their card tricks, stating that “Johnson’s result introduces new ideas and techniques that will surely be of help in other graph cycle problems.”

Diaconis and Graham conclude their article with a testament to the workshop’s success, citing progress made on old conjectures and new conjectures posed, but mostly, focusing on the community that was formed as a result of the time these researchers spent at BIRS. They state, “to find others who think this small world of problems is beautiful and important made a deep impression on all of us.”

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P. DIACONIS and R. GRAHAM, Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks, Princeton University Press (2012), 42-26.

La version française suit ci-dessous. La versión española sigue abajo.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is now accepting proposals for its 2015 program. BIRS will again be hosting a 48-week scientific program at its station in Banff. There is also a possibility (to be confirmed later) that BIRS will be running an additional 20-25 workshops at its developing new station in Oaxaca, Mexico.

The status and state of readiness of the new research station at Oaxaca is still awaiting final commitments from various private and public sponsors. We are aiming to have the facility open and ready to host an augmented BIRS program as soon as 2015. We shall keep the scientific community informed about this exciting potential to increase the BIRS opportunities. For an informal description of the project and its rationale, refer to: http://nghoussoub.com/2013/04/19/tell-me-about-el-casa/

The Station at Banff (and eventually the one in Oaxaca) provides an environment for creative interaction and the exchange of ideas, knowledge, and methods within the mathematical, statistical, and computing sciences, and with related disciplines and industrial sectors. Each week, the station hosts either a full workshop (42 people for 5 days) or two half-workshops (each with 21 people for 5 days). As usual, BIRS provides full accommodation, board, and research facilities at no cost to the invited participants, in a setting conducive to research and collaboration.

Full information, guidelines, and online forms are available at the BIRS website: http://www.birs.ca

The deadline for 5-day Workshop and Summer School proposals is Friday September 27, 2013.

In addition BIRS will operate its Research in Teams and Focused Research Groups programs, which allow smaller groups of researchers to get together for several weeks of uninterrupted work at the station. September 27, 2013 is also the preferred date to apply for these programs. However, proposals for projects involving Research in Teams or Focused Research Groups can be submitted at any time -- subject to availability -- they must be received at least 4 months before their requested start date.

Proposal submissions should be made using the online submission form. Please use: https://www.birs.ca/proposals

Nassif Ghoussoub, Scientific Director,
The Banff International Research Station