You can read about Branton's interests here:
http://www.physics.byu.edu/faculty/campbell/, but many of us will know his extremely elegant work on applying group theory to phase transitions in crystalline materials.
As John Evans showed in his seminar just before Christmas, Branton's methods enable complex distorted structures to be modelled using a high-symmetry 'parent' structure plus a relatively small number of distortion modes.
Possible modes can be derived using group theory in a similar way to the analysis of the normal vibrational modes of molecules. These methods have transformed crystal structure analysis, and Branton's talk will be of interest to anyone interested in the way solid state structures respond to external conditions like pressure or temperature.