Mathematical Sciences: Cohomological and Arithmetic Interpretation of Spectra on Certain Symmetric Spaces

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This project is mathematical research in the representation theory of (semisimple) Lie groups. A suitable example of the latter is the group of rotations of a sphere. Groups like this are important because they occur in many areas of mathematics (e.g. geometry, differential equations,algebraic number theory, mathematical physics) as groups of symmetries. Representation theory allows one to take advantage of symmetries in solving problems. More specifically, the situation is that of a Lie group acting on its quotient modulo a lattice, and thus on the space of square-integrable functions on the quotient. The aim is to obtain the multiplicities in this representation of certain irreducible unitary representations of the group, particularly limits of discrete series representations.