THEMATIC PROGRAMS

April 20, 2014
Thematic Program on Discrete Geometry and Applications 2011

Distinguished Lecture Series
ERIK DEMAINE
Massachusetts Institute of Technology

October 12 -- 4:30 p.m
Algorithms Meet Art, Puzzles, and Magic


Sidney Smith Hall, 100 St. George St., Room 2117


October 13 -- 11:00 a.m.
Fields Institute, Room 230
Linkage Folding: From Erdös to Proteins

October 14 -- 11:00 a.m.
Fields Institute, Room 230

Geometric Puzzles: Algorithms and Complexity

October 12 -4:30 p.m
Sidney Smith Hall, 100 St. George St., Room 2117


Algorithms Meet Art, Puzzles, and Magic

When I was six years old, my father Martin Demaine and I designed and made puzzles as the Erik and Dad Puzzle Company, which distributed to toy stores across Canada. So began our journey into the interactions between algorithms and the arts (here, puzzle design). More and more, we find that our mathematical research and artistic projects converge, with the artistic side inspiring the mathematical side and vice versa. Mathematics itself is an art form, and through other media such as sculpture, puzzles, and magic, the beauty of mathematics can be brought to a wider audience. These artistic endeavors also provide us with deeper insights into the underlying mathematics, by providing physical realizations of objects under consideration, by pointing to interesting special cases and directions to explore, and by suggesting new problems to solve (such as the metapuzzle of how to solve a puzzle). This talk will give several examples in each category, from how our first font design led to building transforming robots, to how studying curved creases in origami led to sculptures at MoMA. The audience will be expected to participate in some live magic demonstrations.

October 13 -- 11:00 a.m.
Fields Institute, Room 230

Linkage Folding: From Erdös to Proteins

Linkages have a long history ranging back to the 18th century in the quest for mechanical conversion between circular motion and linear motion, as needed in a steam engine. In 1877, Kempe wrote an entire book of such mechanisms for "drawing a straight line". (In mathematical circles, Kempe is famous for an attempted proof of the Four-Color Theorem, whose main ideas persist in the current, correct proofs.) Kempe designed many linkages which, after solidification by modern mathematicians Kapovich, Millson, and Thurston, establish an impressively strong result: there is a linkage that signs your name by simply turning a crank.
Over the years mathematicians, and more recently computer scientists, have revealed a deep mathematical and computational structure in linkages, and how they can fold from one configuration to another. In 1936, Erdös posed one of the first such problems (now solved): does repeatedly flipping a pocket of the convex hull convexify a polygon after a finite number of flips? This problem by itself has an intriguingly long and active history; most recently, in 2006, we discovered that the main solution to this problem, from 1939, is in fact wrong.
This talk will describe the surge of results about linkage folding over the past several years, in particular relating to the two problems described above. These results also have intriguing applications to robotics, graphics, nanomanufacture, and protein folding.

October 14 -- 11:00 a.m.
Fields Institute, Room 230


Geometric Puzzles: Algorithms and Complexity

I love geometry because the problems and solutions are fun and often tangible. Puzzles are one way to express these two features, and are also a great source of their own computational geometry problems: which puzzles can be solved and/or designed efficiently using computer algorithms? Proving puzzles to be computationally difficult leads to a mathematical sort of puzzle, designing gadgets to build computers out of puzzles. I will describe a variety of algorithmic and computational complexity results on geometric puzzles, focusing on more playful and recent results.


Erik D. Demaine is an professor of Computer Science at the Massachusetts Institute of Technology. His Ph.D. dissertation, a seminal work in the field of computational origami, was completed at the University of Waterloo. This work was awarded the Canadian Governor General's Gold Medal from the University of Waterloo and the NSERC Doctoral Prize, 2003, for the best Ph.D. thesis and research in Canada (one of four awards). In 2003 he was awarded a MacArthur Fellowship. He joined the MIT faculty in 2001, at age 20, reportedly the youngest professor in the history of the Massachusetts Institute of Technology. He is a member of the Theory of Computation group at MIT Computer Science and Artificial Intelligence Laboratory. Mathematical origami artwork by Erik and Martin Demaine was part of the “Design and the Elastic Mind” exhibit at the Museum of Modern Art in 2008 and has been included in the MoMA permanent collection.


Speakers in the Distinguished Lecture Series (DLS) have made outstanding contributions to their field of mathematics. The DLS consists of a series of three one-hour lectures.
Index of Fields Distinguished and Coxeter Lectures


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