Abstract:
In recent years Timo Betcke and I have developed methods for
high-accuracy computation of eigenfunctions of the Laplacian on
planar regions. This talk will present some beautiful images
resulting from these computations, focussing on a collection of
eight examples including L-shaped regions, gaskets with holes,
and infinite channels with kinks and elbows. It is remarkable
how many physical phenomena can be seen in such results, and in
particular, we shall relate eigenfunctions of drums of various
shapes to the Nobel Prizes in Physics awarded in 1902, 1903,
1907, 1909, 1918, 1919, 1933, 1952, 1963, 1964, 1977, and 1981.