04/20/2016 - 12:00am

Congratulations to Professor Zhiqin Lu and his collaborator, Julie Rowlett from Chalmers University in Gothenburg, Sweden. They received the Halmos-Ford ​Award from the Mathematical Association of America for their paper "The Sound of Symmetry," published in the November 2015 issue of The American Mathematical Monthly. The Halmos-Ford Award recognizes authors of articles of expository excellence published in The American Mathematical Monthly. The award will be presented at MathFest 2016.

Award Committee Citation: Beginning with M. Kac's 1966 article in The Monthly “Can one hear the shape of a drum?", the authors of this lovely article present “an interactive introduction to inverse spectral theory.” They entice the reader from the start with the promise that the article will explain the answer to Kac's question while simultaneously challenging the reader to complete exercises. Along with the history of this fruitful area of mathematics the reader builds up intuition from the answers to questions like “Can you hear the shape of a string?" and exercises like “Prove that you can hear the shape of a rectangle.” The main techniques of inverse spectral theory are introduced with careful discussion and motivation. These techniques are then applied to prove that one can hear the shape of parallelograms, acute trapezoids, and regular n-gons. The authors show that one can “realistically hear the shape of the regular n-gon amongst all convex n-gons because it is uniquely determined by a finite number of eigenvalues; the sound of symmetry can really be heard!" With this very thorough, inspiring, and carefully constructed foundation laid out, the authors leave the reader at the end of the paper with a collection of natural and intriguing open problems and conjectures to consider.