CAREER: Multiple Dirichlet series and metaplectic groups

“该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。“近年来，在Weyl群多重Dirichlet级数领域有一系列的活动。 这些多重狄利克雷级数和几个不同的数学领域之间出现了令人惊讶和意想不到的联系。 PI一直站在发展一般理论和识别这些联系的最前沿。 他将追求的进一步发展，导致新的应用相互关联的数论，自守形式，表示理论的metaplectic群和理论的仿射和无限的根系统。这些活动将有助于把相对较新的领域外尔群多重狄利克雷级数到一个更中心的位置，在现代数学。因此，正达公司将进行的研究项目将引起许多不同领域专家的兴趣。 在多重狄利克雷级数的新应用中， * Casselman-Shalika公式的一个元形式（在 不存在多重性1） * Eisenstein级数正交周期的一个公式 编码经典形式的深层和经典属性，例如 一个最简单的新发现的情况相当于高斯的三个平方 定理 * 字符之间的连接对函数字段求和 仿射根系的性质结合提议人的研究活动，他将继续指导本科生和高中生。 纽约城市学院是一所公认的少数族裔服务机构，拥有由西班牙裔（37\%），黑人（26\%），亚洲（20\%）和白色（12\%）学生组成的多元化本科生群体。 提议者将向这些学生介绍研究水平的数学。 此外，提议者还与哈莱姆儿童协会合作，指导来自代表性不足社区的高中生。位于哈莱姆，城市学院是在一个独特的位置，使该地区的学生体验在数学和科学前沿研究服务于其社区。 这项CAREER赠款将有助于扩大这种伙伴关系的范围。

"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 systemsIntegrated 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 experiencecutting edge research in mathematics and the sciences. This CAREERgrant will help extend the scope of this partnership.