9415549 Tesanovic This project deals with the theory of superconductivity in high magnetic fields. In high fields, the standard theory of superconductivity has qualitative and dramatic deviations. Entirely new, strong fluctuation, theoretical approaches are developed. The theory of coherent, gapless, quasipartical bands formed by closely spaced, high-field vortices is studied. Resolving these deep theoretical issues is likely to result in new physical concepts and ideas which can be applied to a variety of other problems. %%% Many applications of superconductors, from manufacturing applications to high-performance magnets, involve the coexistence of superconductivity and high magnetic fields. The standard theory of superconductivity no longer applies for very large fields. In this project the theory of superconductivity in such fields is developed. This work will relate to recent experimental activity concerning the conditions under which materials will be superconductors. It will also compliment NSF's strong commitment to the exploration of the high magnetic field frontier, embodied in the National High Magnetic Field Laboratory. ***