Computer Assisted Mathematics

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The investigators propose to carry out computer - assisted research in mathematics. Several projects are proposed in which computers will play a crucial role: in working out examples, in helping to formulate and test significant conjectures, and in actually carrying out key computational steps of proofs of theorems that are not feasible to do by hand. Areas of interest include; 1. Large simple groups, knots, partisan games, lattices and sphere-packing. 2. The stability of matter. 3. The equidistribution of exponential sums over finite fields. While these areas represent disparate (but not disjoint) mathematical disciplines, the unifying and compelling aspect is the need for computational and technical resources that the investigators can share.