Minimal Representations and Theta Correspondence

这笔赠款将为美国的参与者提供支持，以参加为期五天的研讨会，题为“最低限度的代表和θ对应”，将在欧文薛定谔研究所（ESI）在维也纳，奥地利举行。 活动将于2022年4月11日至15日举行。 在会议上讨论的最小表示主题在数学中发挥了中心和统一的作用超过50年，在那里他们发现应用到量子力学和通信理论，并在数学数论。 Theta对应使用最小表示来连接不同的数学对象。 最近，关于θ对应的工作加速了，豪的对偶猜想的完整证明就在几年前发表了。该奖项将允许美国学者继续在全球舞台上与国际研究人员一起研究最小表示和θ对应，并向新一代数学家介绍材料。最小表示可应用于自守形式，调和分析，例如，基本仿射空间上的傅立叶变换，以及数学物理，例如，弦理论中的散射振幅 它们起源于元群的韦尔表示，在那里它们通过波函数与薛定谔的量子力学公式相联系。 在数学中，最小表示的最深刻的应用是通过theta对应--豪对偶对应的推广。 更新的“特殊”θ对应在朗兰兹纲领和算术中至关重要。 这次会议是一个及时的事件，使与会者最新的最小表示和theta对应的最新突破。 ESI研讨会将汇集来自世界各地的顶尖学者，展示数学这一领域的最新进展，赠款将允许美国学者前往奥地利参加这一重要活动。 有关会议的更多信息，请参阅https://www.esi.ac.at/events/e420.This奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。

This grant will provide support for U.S. based participants to attend a five day workshop titled "Minimal Representations and Theta Correspondence," to be held at the Erwin Schrödinger Institute (ESI) in Vienna, Austria. The event will take place April 11-15 2022. The minimal representations topics discussed at the conference have played a central and unifying role in mathematics for over fifty years, where they find applications to quantum mechanics and communication theory, and within mathematics to number theory. Theta correspondences use minimal representations to connect disparate mathematical objects. Work on theta correspondences has accelerated recently, with the full proof of Howe's Duality Conjecture published just a few years ago. The award will allow U.S. scholars to continue working on minimal representations and theta correspondences on the global stage, with an international community of researchers, as well as introduce a new generation of mathematicians to the material.Minimal representations have applications to automorphic forms, harmonic analysis, for example, the Fourier transforms on basic affine spaces, and mathematical physics, for example, scattering amplitudes in string theory. They originate in the Weil representation of the metaplectic group, where they are connected to Schrödinger's formulation of quantum mechanics via wave functions. Within mathematics, the most profound applications of minimal representations are through theta correspondences -- a generalization of Howe's duality correspondence. Newer "exceptional" theta correspondences have been vital in the Langlands program and arithmetic. This conference is a timely event, bringing participants up-to-date on recent breakthroughs on minimal representations and theta correspondences. The ESI workshop will bring together the top scholars from around the world to showcase the latest progress in this field of mathematics and the grant will allow U.S. scholars to travel to Austria and attend this important event. For more information on the conference, see https://www.esi.ac.at/events/e420.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.