Research in theoretical elementary particle physics will try to improve our understanding of large effects in quantum chromodynamics, the theory which describes the strong nuclear force. The role of topology in explaining such phenomena as the confinement of quarks inside nucleons will be investigates. Calculations will also be done to study `duality` relations between seemingly unrelated theories. The methods to be used will approximate the space- time continuum by a discrete lattice of points. The problems to be addressed are important to our understanding of how the strong nuclear force produces some of its most dramatic effects.