The motivations, goals and general culture of theoretical physics and mathematics are different. Most practitioners of either discipline have no necessity for m

This volume, based on lectures and short communications at a summer school in Villa de Leyva, Colombia (July 2005), offers an introduction to some recent develo

This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles written by top experts in low-dimensional t

These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. Whi

The remarkable developments in differential topology and how these recent advances have been applied as a primary research tool in quantum field theory are pres