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Neal Buccino, Associate Director of Public and Media Relations, Rutgers University-New Brunswick and RBHS notes, Rutgers mathematician co-hosts a workshop on higher dimensional geometry.
Circle Limit IV (Heaven and Hell), 1960, by M. C. Escher.
Photo: WikiArt
The artist M. C. Escher brought complex mathematical ideas to life through dizzying illustrations like Circle Limit IV (Heaven and Hell), in which angels and demons soar through an infinite, bowl-shaped space. Their winged bodies form a pattern that mathematicians call a lattice.
In December, a Rutgers University-New Brunswick mathematician will co-host a workshop, convened by the American Institute of Mathematics and National Science Foundation, to ask, among other things: How would those angels and demons look if Escher’s drawing were 22-dimensional? Or 1,001-dimensional? Or in any number of other dimensions?
Welcome to the world of “hyperbolic reflection groups,” the name for the type of geometric space Escher depicted in his Circle Limit engravings. They represent what you’d see if you placed a single object – say a single angel-devil picture – at the bottom of a bowl and surrounded it by mirrors to make the image reflect itself, over and over, infinitely...
Kontorovich and the workshop’s other mathematicians, representing the fields of geometry, topology, dynamics, arithmetic groups and number theory, intend to find out. The effort may take years, and what they learn might benefit other branches of mathematics.
