Plenary Lecture
Spectral Structure of the Equilateral Triangle
Professor Brian J. McCartin
Department of Mathematics,
Kettering University,
Flint, Michigan USA
Abstract: Lame’s formulas for the eigenvalues and eigenfunctions
of the Laplacian on an equilateral triangle with Dirichlet and Neumann boundary conditions will be
reviewed and then extended to the Robin boundary condition. The eigenfunctions will be shown to form
a complete orthonormal system. Various properties of the spectrum and modal functions will be explored.
About the speaker: Brian McCartin received his B.S. (with Highest
Distinction) and M.S. in Mathematics from University of Rhode Island, and his Ph.D. in Applied Mathematics
from NYU's Courant Institute of Mathematical Sciences. He also holds the degree of Bachelor of Music
(Summa Cum Laude) from the Hartt School of Music at the University of Hartford. In 2000, he was the
recipient of Kettering University's Outstanding Researcher Award and received their Outstanding Teaching
Award in 2001 and again in 2006. He was the 2004 recipient of the Award for Distinguished College or
University Teaching of Mathematics from the Michigan Section of the Mathematical Association of America.
Prior to joining the Kettering University faculty in 1993, he was Senior Research Mathematician for United
Technologies Corporation and chairman of Computer Science at Rensselaer Polytechnic Institute’s Hartford, CT
campus. He serves on the Editorial Board of the international journal Applied Mathematical Sciences and is a
Fellow of the Electromagnetics Academy.