Professor Erica Flapan Inducted Into the Inaugural Group of Fellows of the American Mathematical Society
Erica Flapan, the Lingurn H. Burkhead Professor of Mathematics, was recently inducted into the inaugural group of Fellows of the American Mathematical Society, which recognizes “members who have made outstanding contributions to the creation, exposition, advancement, communication, and utilization of mathematics."
In addition in 2011, Flapan was one of three winners nationwide of the Mathematical Association of America’s Haimo Award for distinguished teaching, which was established "to honor college or university teachers who have been widely recognized as extraordinarily successful and whose teaching effectiveness has been shown to have had influence beyond their own institutions.” Another recent honor was the inclusion of her 2011 College Mathematics Journal article, “How to be a good teacher is an undecidable problem,” in the volume The Best Writing on Mathematics 2012 (Princeton University Press, 2012), edited by Mircea Pitici.
Flapan has been at Pomona College since 1986. Her field of research is in the area of topology known as “spatial graph theory,” which studies the topology of graphs embedded in three-dimensional space. Topology, which studies the properties of spaces and figures which are preserved under continuous deformations, was developed to study supercoiling, knotting and catenation of DNA and to analyze the structure of non-rigid molecules, which are modeled as graphs embedded in three-dimensional space.
She has worked in this interdisciplinary area for more than 25 years, applying topological methods to problems in chemistry and molecular biology. While many of her publications are about the topological structure of arbitrary graphs, most of her work is either motivated by or closely related to the study of the topology of large molecules.
Her recent work has been on classifying the symmetries of flexible molecules. Chemists normally use the group of rigid symmetries of a molecule (known as the “ point group”) to classify molecular symmetries. While the symmetries of most molecules can be represented by their rotations, reflections, and rotations combined with reflections, large molecules have greater flexibility and hence some of their symmetries may not be the result of a rigid motion.
For such molecules, a topological rather than a geometric approach makes sense. Flapan has been a leader in the use of the “topological symmetry group” as a way of classifying the symmetries of these molecules, and has obtained many results on which groups can and cannot occur as topological symmetry groups. She was invited to give a plenary address at an American Mathematical Society meeting on her work on topological symmetry groups, and this led to her selection as an inaugural AMS fellow.
The American Mathematical Society and the Mathematical Association of America are national professional organizations of mathematicians with different missions. The mission of the AMS is “to further the interests of mathematical research and scholarship,” whereas the mission of the MAA is "to advance the mathematical sciences, especially at the collegiate level."