superconductivity in the cuprate materials. Elected to the U.S. National Academy of Sciences, 2014. The citation reads: Sachdev has made seminal advances in the theory of condensed matter systems near a quantum phase transition, which have elucidated the rich variety of static and dynamic behavior in such systems, both at finite temperatures and at T=0. His book, Quantum Phase Transitions, is the basic text of the field. Abdus Salam Distinguished Lecturer, International Center for Theoretical Physics, Trieste, Italy, 2014. Hendrik Lorentz Chair, Lorentz Institute, 2012. Perimeter Institute for Theoretical Physics Distinguished Research Chair, 2009-14. John Simon Guggenheim Memorial Foundation Fellow, 2003. Fellow of the American Physical Society "for his contributions to the theory of quantum phase transitions and its application to correlated electron materials". Alfred P. Sloan Foundation Fellow, February 1989. LeRoy Apker Award Recipient, 1982. Research Quantum phases of antiferromagnets Sachdev has worked extensively on the quantum theory of antiferromagnetism, especially in two-dimensional lattices. Some of the spin liquid states of antiferromagnets can be described by examining the quantum phase transitions out of magnetically ordered states. Such an approach leads to a theory of emergent gauge fields and excitations in the spin liquid states. It is convenient to consider two classes of magnetic order separately: those with collinear and non-collinear spin order. For the case of collinear antiferromagnetism (as in the Néel state), the transition leads to a spin liquid with a U(1) gauge field, while non-collinear antiferromagnetism has a transition to a spin liquid with a Z2 gauge field. The U(1) spin liquid is unstable at the longest length scales to the condensation of monopoles, and the Berry phases of the condensing monopoles lead to valence bond solid (VBS) order. The Z2 spin liquid was shown to be stable, and this was the first realization of a stable quantum state with time-reversal symmetry, emergent gauge fields, topological order, and anyon excitations. The topological order and anyons were later identified with the e, m and ε particles of the toric code (see also the independent work of Xiao-Gang Wen). Sachdev was the first to identify that Z2 spin liquids come in two classes: `even' and `odd'. Half-integer-spin antiferromagnets can only realize odd Z2 spin liquids, which therefore provide a theory for Anderson's RVB state. Odd Z2 spin liquids have (what is now called) an anomaly which constrains the symmetry transformations of the anyon excitations, and modifies the anyon condensation