论文标题
模块化形式和字符串的讲座
Lectures on modular forms and strings
论文作者
论文摘要
这些讲座的目的是向数字理论和弦理论中的概念和兴趣的方法提出非正式但精确的介绍，这些概念和弦理论围绕模块化形式及其概括。模块化不变性在于，在IIB型超串线理论中，链式摄动理论，弦扰理论，蒙顿 - olive双重性，seiberg-witten理论和s偶性的核心。相对于较高的算术组以及模块化模块形式的自多态形式进入环形弦弦压缩和黑洞微晶体的计数。在介绍了基本的数学概念，包括椭圆函数，模块化形式，MAASS形式，一致性亚组的模块化形式，矢量值值模块化形式和模块化图形形式后，我们描述了无数次申请中对数学和物理学中的问题的一小部分，包括上述数学和物理学。
The goal of these lectures is to present an informal but precise introduction to a body of concepts and methods of interest in number theory and string theory revolving around modular forms and their generalizations. Modular invariance lies at the heart of conformal field theory, string perturbation theory, Montonen-Olive duality, Seiberg-Witten theory, and S-duality in Type IIB superstring theory. Automorphic forms with respect to higher arithmetic groups as well as mock modular forms enter in toroidal string compactifications and the counting of black hole microstates. After introducing the basic mathematical concepts including elliptic functions, modular forms, Maass forms, modular forms for congruence subgroups, vector-valued modular forms, and modular graph forms, we describe a small subset of the countless applications to problems in Mathematics and Physics, including those mentioned above.
