Geometry: education, art, and research (GEAR 2021)

Abstract

It is no exaggeration to say that Banff, Alberta, Canada is one of the most beautiful places on earth. The town sits within a Canadian national park and is surrounded by mountains on all sides. The slope of Tunnel Mountain is home to the Banff Centre for Arts and Creativity, a world-famous institute for visual, literary, and performing arts. And, in a stroke of good fortune that exceeds all expectations, the campus also hosts the Banff International Research Station (BIRS), a facility for research workshops in mathematics and related disciplines. I have attended a handful of events at BIRS over the years. I would take in the mountain vista from the dining hall, and look out the windows of lecture rooms to see deer grazing outside. After a day of mathematical discussion, I would often attend recitals by some of the young virtuosos studying at the Centre. All of this is to say that, amid all the chaos of the past twelve months, it was especially bittersweet to be invited to participate in an event hosted by BIRS, but not at BIRS. Overall I have appreciated the respite from work-related travel, but I would have liked a chance to visit Banff again. I was nevertheless delighted to have received an invitation to participate in the BIRS workshop entitled Geometry: Education, Art, and Research (GEAR 2021), held virtually over the weekend of February 19th, 2021. Targeted primarily at individuals in secondary and post-secondary education, the goal was to foster interaction between the three groups represented in the title (educators, artists, and researchers), on topics loosely related to geometry. If nothing else, it promised to be a good opportunity to connect with far-flung friends from the mathematical art world. And make no mistake: while the online format has unfortunate limitations that undermine the primary social goals of conferences, it also offers a few distinct advantages. First, it changes the pattern of attendance. A typical 2-day workshop at BIRS can host at most 25 participants. And while accommodations are provided, participants must cover their own travel and food costs. Attendance is therefore typically limited to academics with research support. GEAR 2021 brought together 66 confirmed participants, including a few artists who likely would not have been able to attend otherwise. The only real barrier to attendance would be too great a difference in time zones, given that the workshop operated on Mountain Time. See Figure 1 for a virtual group photo. Ther other advantage to meeting online is that, without much extra effort, the meeting can leave behind a large digital footprint. Most presentations were recorded, and