THE REES DISTINGUISHED LECTURER SERIES

Dr. Nick Trefethen

 Oxford University

"Confessions of a number cruncher"

Thursday April 17, 2003

3:30 - 4:30 205 Kirkbride Hall

Before computers, most mathematical problems could not be solved. Now they can be, and science and engineering have changed utterly. But it's not computers alone that solve mathematical problems: it is computers programmed to implement the algorithms of numerical analysis, most of which did not exist a century ago. Amazing changes have taken place in the number crunching business in the past fifty years, and they are full of philosophical twists and turns and puzzles and surprises. They also give hints of what may be in store for our sciences and our computations in the next fifty.

This is a general lecture for a general audience. 

"Eigenmodes of polygonal drums"

Friday April 18, 2003

3:30 - 4:30 104 Gore Hall

Many questions of interest to both mathematicians and physicists relate to the behavior of eigenvalues and eigenmodes of the Laplace operator on a polygon. Algorithmic improvements have revived the old "method of fundamental solutions"; is it now competitive with the state-of-the-art method of Descloux, Tolley and Driscoll? This talk will outline the numerical issues but give equal attention to applications including "can you hear the shape of a drum?", localization of eigenmodes, eigenvalue avoidance, and the design of drums that play chords.

This is a lecture for a general mathematical audience.