RECENT DEVELOPMENTS IN THE THEORY OF THE QUANTUM HALL-EFFECT

The past few years have produced major advances in our understanding o f the quantum Hall effects - quantized and unquantized. Theories based on a mathematical transformation, where the electrons are replaced by a set of fermions interacting with a Chern-Simons gauge field, have b een useful for explaining and predicting observations at even-denomina tor filling fractions where quantized Hall plateaus are not observed, as well as for giving new insight into the most prominent fractional q uantized Hall states at odd-denominator fractions. Other theoretical a pproaches have led to important advances in our understanding of edge- excitations for systems in a fractional quantized Hall state, of phase s and phase transitions in bilayer systems, of tunneling phenomena in the quantum Hall regimes, and of disorder-induced transitions between ''neighboring'' quantum Hall plateaus. Some highlights of these develo pments are reviewed.