"This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5)."
In recent years there has been a flurry of activity in the field of Weyl group multiple Dirichlet series. Surprising and unexpected connections between these multiple Dirichlet series and several different fields of mathematics have emerged. The PI has been at the forefront of the development of the general theory and identification of these connections. He will pursue the further developments which lead to new applications interrelating number theory, automorphic forms, the representation theory of metaplectic groups and the theory of affine and infinite root systems. These activities will serve to place the relatively new field of Weyl group multiple Dirichlet series into a more central position in modern mathematics. As such, the research projects Chinta will undertake will interest specialists in many different fields. Particularly striking among the new applications of multiple Dirichlet series are * A metaplectic version of the Casselman-Shalika formula (in the absence of multiplicity one) * A formula for orthogonal periods of Eisenstein series which encodes deep and classical properties of classical forms, e.g. the simplest new case discovered is equivalent to Gauss's three squares theorem * Connections between characters sums over function fields and characters of affine root systems
Integrated with the research activities of the proposer will be his continued mentorship of undergraduate and high school students. City College of New York is a recognized minority serving institution with a diverse undergraduate student body consisting of Hispanic (37%), Black (26%), Asian (20%) and White (12%) students. The proposer will introduce these students to research level mathematics. In addition, the proposer has entered into a collaboration with the Harlem Children's Society, in order to mentor high school students from underrepresented communities. Situated in Harlem, City College is in a unique position to serve its community by enabling area students to experience cutting edge research in mathematics and the sciences. This CAREER grant will help extend the scope of this partnership.
