Research Interests

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.

Membership Type


Election Year


Primary Section

Section 32: Applied Mathematical Sciences

Secondary Section

Section 11: Mathematics