Conference: Solvable Lattice Models, Number Theory and Combinatorics

该奖项支持美国研究人员参加将于2024年6月24日至26日在都柏林三一学院汉密尔顿数学研究所举行的可解晶格模型、数论和组合学会议。可解晶格模型首先出现在物理相变的描述中，并已成为数学中有用的工具。在过去的几年里，一组研究人员发现，它们可以用来有效地模拟数论和代数组合中的数量。与此同时，其他学者使用来自表征理论的不同方法来研究这些量。这次会议将是一个展示这些发展的场所，并将使用不同方法研究相关问题的研究人员和有兴趣了解更多相关知识的学生聚集在一起。本次会议重点讨论了p进群和覆盖群上的可解晶格模型和特殊函数之间的新联系，量子群、Hecke代数和其他方法的使用，以研究p进群及其覆盖的表示，以及代数组合学和代数几何的进展。球面函数和Iwahori Whittaker函数就是这种特殊函数的例子，在许多领域发挥着重要作用。本次会议的网站是https://sites.google.com/bc.edu/solomon-friedberg/dublin2024.This，该奖项反映了美国国家科学基金会的法定使命，并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，认为值得支持。

This award supports the participation of US-based researchers in the Conference on Solvable Lattice Models, Number Theory and Combinatorics that will take place June 24-26, 2024 at the Hamilton Mathematics Institute at Trinity College Dublin. Solvable lattice models first arose in the description of phase change in physics and have become useful tools in mathematics as well. In the past few years a group of researchers have found that they may be used to effectively model quantities arising in number theory and algebraic combinatorics. At the same time, other scholars have used different methods coming from representation theory to investigate these quantities. This conference will be a venue to feature these developments and to bring together researchers working on related questions using different methods and students interested in learning more about them.This conference focuses on new and emerging connections between solvable lattice models and special functions on p-adic groups and covering groups, uses of quantum groups, Hecke algebras and other methods to study representations of p-adic groups and their covers, and advances in algebraic combinatorics and algebraic geometry. Spherical and Iwahori Whittaker functions are examples of such special functions and play an important role in many areas. The website for this conference is https://sites.google.com/bc.edu/solomon-friedberg/dublin2024.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.