Mathematical Sciences: Intertwining Operators, R-groups and Automorphic L-Functions

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This award supports research in number theory and representation theory. The principal investigator will work on determining the poles of standard intertwining operators attached to arbitrary maximal parabolic subgroups of quasi-split unitary groups and special orthogonal groups in odd dimensions. He will also continue research on the tempered spectrum of similitude groups. This award also supports the principal investigators efforts to establish a series of courses in number theory and representation theory. Number Theory is the study of properties of the whole numbers and is the oldest branch of mathematics. From the beginning problems in number theory have furnished the driving force to create new mathematics in almost all parts of the discipline. The Langland's program is a general philosophy that connects number theory with calculus. Modern number theory is very technical and deep, but has had astonishing applications in areas like theoretical computer science and coding theory.