Naval Academy Professor Will Talk on “From Linking Numbers to Lights Out” Wednesday

Mark Kidwell, a mathematics professor at the U.S. Naval Academy who is conducting research at Lafayette, will give a talk on “From Linking Numbers to Lights Out” noon Wednesday in Pardee Hall room 227.

Open to the campus community, the talk is part of the math department’s Mathematical Adventures and Diversions (MAAD) series. Lunch will be provided.

MAAD is a series of talks on mathematical topics and applications that are often not encountered in mathematics courses. They are open to the Lafayette community and assume no special mathematical preparation on the part of the audience.

Kidwell’s presentation concerns a situation similar to the game Lights Out, in which pressing a button to change one light in a rectangular array also changes the status of neighboring lights.

“In a link of c circles in three-space, you can assign an integer to each pair of circles called the linking number,” he explains. “Before you can talk about positive and negative linking numbers, you have to put an arrow (orientation) on each of your circles. In a famous table of knots and links, Bailey and Roth neglected to put arrows on their circles. The question arises: Can you add arrows in a way that will make all c-choose-2 of your linking numbers positive? Reversing the arrow on one circle alters the signs of all the linking numbers involving that circle.”

Kidwell studies knots, links, and braids. He received his Ph.D. in 1976 from Yale University under the direction of Ronnie Lee. He has taught at Amherst College and the U.S. Naval Academy, and taken sabbaticals at Columbia, Liverpool, and George Washington Universities, and currently at Lafayette. His wife Peggy is also on sabbatical from her position as curator of mathematics at the Smithsonian Institution, and is writing a book about the material culture of mathematics.