The 11th Annual Pi Mu Epsilon Lecture was given by Dr. Ileana Streinu on Nov. 1, 2017.

Streinu is the Charles N. Clark Professor of Computer Science and Mathematics at Smith College. She became a fellow of the American Mathematical Society in 2012 and has been awarded the 2010 Robbins Prize of the American Mathematical Society as well as the 2004 Moisil Prize of the Romanian Academy. In addition, she heads the Laboratory for Research in Kinematics and Geometry, which combines her research in combinatorial and computational geometry with biology and robotics.

Following the induction of 11 new undergraduate members into the Nebraska Alpha chapter of Pi Mu Epsilon, Streinu gave the 11th annual Pi Mu Epsilon address “Maxwell’s Problem, 150 years later: from bridges to nano-mechanics.”

While the physicist James Clerk Maxwell is best known for his contributions to electromagnetism, Maxwell the mathematician is notable for writing two geometry papers. Maxwell’s papers form the basis for the study of bar and joint frameworks and the interplay between rigidity and flexibility. These frameworks can be represented as graphs, and their rigidity or flexibility refer to the possible embeddings of the graphs in space. While redundant rigidity is desirable for architectural structures like bridges, flexibility is essential for nano-structures appearing in biology. In fact, some flexible structures can model the behavior of viruses, which must have enough flexibility to release their toxic load. In dimensions 1 and 2, a necessary and sufficient condition can be given for minimal rigidity of frameworks based solely on the density of edges. While this necessary condition holds in higher dimensions, it is not sufficient, which leaves Maxwell’s problem, now a 150-year-old problem, still open to this day.

Streinu also discussed her own extension of this problem to infinite periodic structures. By solving an analogue of Maxwell’s problem for period and symmetry group respecting embeddings, Streinu and her collaborators were able to find a family of designs for auxetic materials, special structures that expand in a perpendicular direction as they are stretched. This property, while somewhat rare in nature, is familiar to children worldwide as a property of the Hoberman sphere, a colorful toy which expands from a star to a sphere via movement in one direction.

One of the important objectives of the Pi Mu Epsilon lecture series is to provide an opportunity for math major undergraduates to meet a distinguished professor from another university who can provide a glimpse into their area of mathematics. The series is organized by the Nebraska Alpha Chapter of Pi Mu Epsilon, currently celebrating the 89th anniversary of its founding, and is supported by the Department of Mathematics and the Nebraska Math Scholars program.

– Corbin Groothuis and Alexandra Seceleanu