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Trinity学院汉密尔顿数学研究所举行的可解格模型，数论和组合数学会议。 可解格点模型最早出现在物理学中对相变的描述中，并已成为数学中的有用工具。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学中出现的量。与此同时，其他学者也使用了来自表征理论的不同方法来研究这些量。 本次会议将是一个场地，以功能这些发展，并汇集研究人员在相关问题上使用不同的方法和学生有兴趣了解更多关于他们的工作。本次会议的重点是新的和新兴的可解格模型之间的联系和特殊功能的p-adic群和覆盖群，使用量子群，Hecke代数和其他研究p进群的表示及其覆盖的方法，以及代数组合学和代数几何学的进展。 球面函数和岩堀惠特克函数就是这类特殊函数的例子，在许多领域中起着重要的作用。这次会议的网站是https://sites.google.com/bc.edu/solomon-friedberg/dublin2024.This奖反映了NSF的法定使命，并已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的支持。

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.