Potts Models, Chromatic Polynomials, the Four-Color Problem,
New York University
November 2, 2006
Pizza and Beverages at 12:30 pm
The chromatic polynomial was introduced by Birkhoff in 1912 in connection with the famous Four-Color Conjecture. The same polynomial arises in statistical mechanics in connection with the Potts model, and it has been of great interest to both physicists and mathematicians for many years. Indeed, as Yang and Lee showed in 1952, phase transitions in the physical Potts model correspond to the zeros of the chromatic polynomial. I will begin by giving an introduction to these problems and then sketch some recent results and open problems. This talk is intended to be understandable to both physics and mathematics students; no prior knowledge of either graph theory or statistical mechanics is required.
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