Mathematical Sciences: Representation Theory and Differential Geometry

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The principal investigator will study the implications in mathematical physics of the minimal representation of SO(4,4), completely integrable systems using "pairs of Hamiltonian operators," G-invariant differential operators on the nil-cone, and Lusztig's basis theorem. The project to be undertaken by the principal investigator involves techniques from group theory and will have consequences in mathematical physics. A group is an abstract algebraic concept which simply involves a collection of numbers or variables and a prescribed manner of combining them which obeys certain rules. The integers with the operation of addition is an example of a group. By the 1970s mathematical physicists understood that relationships between subatomic particles could be described using the group theory which had been studied for many years by algebraists.