Desmond stated that Kelvin was the sole operator of the Swan research station and that he had died, leaving Desmond to push the 'button' in the Hatch.
Cultural references
Kelvin is also the name of the main character in Stanisław Lem's book "Solaris". In this book, astronauts are sent to a planet that makes elements from their memories materialise. E.g. Kelvin's dead wife comes and visit him in the space station. This bears some similarities with the appearances of Jack's dead father in season 1 and Hurley's imaginary friend Dave in season 2. Just like planet Solaris, the island might make elements from the survivors' unconscious come (physically) true.
Kelvin is the SI's (International System of Units) unit of temperature
One of the scientific mysteries of superconductors is that they do not have sharply defined Critical Temperatures. Typically, the transition from normal to superconducting state takes place over a range of about 5 degrees Kelvin. One critical temperature that falls in this range with a reading of about 94 Kelvin for YBa2Cu3O7, and about 108 Kelvin for Bi2Sr2Ca2Cu3O10.
In James P. Blaylock's novel "Lord Kelvin's Machine," Lord Kelvin invented an electromagnetic device which would negate the earth's magnetic field for a brief time in order to avoid a collision with an iron-bearing comet. The hero spends the first part of the novel trying to prevent the machine from being turned on, as the result would be cataclysmic. Also of note, the book, which takes place in an alternate Victorian era, makes use of Maxwell's Equations, a series of equations that describe gravity and magnetism. In the real world, Maxwell only came up with 4 equations. To account for all the impossible science that exists in the alternate world, Blaylock had his Maxwell come up with an additional 12 laws, bringing the total to a Swan friendly 16.
