APS Medal for Exceptional Achievement in Research: Topology and Other Tools in Condensed Matter Physics*

Notions from topology have played a big role in our current understanding of both classical and quantum systems, and much of my work has been related, in one way or another, to topological ideas. However, topology has only been one tool in my research, sometimes as a starting point and sometimes an afterthought. Other ingredients have included ideas from statistics and quantum mechanics, and analyses of interaction energies and the effects of topological defects on other variables of a system. One portion of my work has focused on phase transitions that could be understood in terms of a proliferation of topological defects, and on dynamic properties that could be understood by the motion of such defects. Other portions of my work have made important use of notions of percolation. My work on quantum Hall systems, at least in retrospect, has always been related to notions of topology in Hilbert space. In my talk, I will present some examples of these applications.