Michael Aizenman

My primary research area is mathematical analysis of phenomena exhibited by systems with many degrees of freedom, classical and quantum. Topics which have attracted particular attention include: critical behavior in classical and quantum statistical mechanics; the structure of the related field theories; effects of disorder on the nature of phase transitions; analysis of Schroedinger operators; and quantum localization effects of disorder. The objective has been the development of rigorous methods which permit to answer qualitative questions even in the absence of exact solutions. A theme recurring in different forms is the appearance of stochastic geometric effects which play important roles in the behavior of critical system. Current work includes a new look at the mathematical description of fractal structures affecting the scaling limit and the emergence of conformal invariance in critical percolation models, spin systems, and related field theories.