Mathematical Sciences: A Stable Trace Formula for the Rank-Two Symplectic Group

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Hales This award supports the work of Professor Thomas Hales in the Langland's Program. The Langland's Program is central to modern number theory by providing structure to the idea that discrete geometric information can be studied analytically. Prof. Hales works on establishing special cases of the trace formula. He is also interested in studying some unsolved problems in real groups. These problems are of interest in a number of different areas of mathematics. This research falls under the general heading of Number Theory. Number Theory is the study of the 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 creation of 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 it has had astonishing applications in areas like theoretical computer science and coding theory. ***