VPW: Visiting Professorships for Women: Theta Series and Automorphic Forms

在最近的工作中，林恩·沃林博士对西格尔的表示公式进行了代数证明，给出了比西格尔的公式更明确的公式来描述偶数阶和奇数阶正定二次型的平均表示数。她目前正在与J.L. Hafner合作，利用自同构形式理论将这些结果推广到不定二次型，得到了不定形式在数域和函数域上表示的显式公式。在与O. Imamoglu的合作中，Walling博士定义了函数场上的辛函数并计算了变换公式，并将在函数场设置中发展一些西格尔模形式和雅可比形式的理论。将通过高维二次型获得关于二次型表示的信息。她还打算扩展与J. Hoffstein和K.D. Merrill合作开发的技术，明确地计算权值为0和1/2的尖形式的傅里叶系数，这些同余子群只允许尖形式的一维空间。互动活动包括开发基于思考、精确推理和清晰沟通的大学数学课程；为女数学家建立一个夏季研究所；为女性举办为期一周的谐波分析和数论会议。

In recent work, Dr. Lynne Walling developed an algebraic proof of Siegel's representation formula, yielding formulas more explicit than those of Siegel to describe average representation numbers of positive definite quadratic forms of even rank and odd level. She is currently working with J.L. Hafner, using the theory of automorphic forms to extend these results to indefinite quadratic forms, obtaining explicit formulas for the measures of the representations of the indefinite forms over number fields and over function fields. In work with O. Imamoglu, Dr. Walling has defined a symplectic theta function over a function field and computed the transformation formula nd will develop some theory of Siegel modular forms and Jacobi forms in the function field setting. Information will be gained regarding representations of quadratic forms by higher dimensional quadratic forms. She also intends to extend the techniques developed in work with J. Hoffstein and K.D. Merrill, explicitly computing the Fourier coefficients of cusp forms of weights 0 and 1/2 for congruence subgroups that admit only one-dimensional spaces of cusp forms. Interactive activities include developing curricula for college/university mathematics courses based on contemplation, precise reasoning and clear communication; developing a summer research institute for women mathematicians; and running a one-week conference for women in harmonic analysis and number theory.