Representation Theory and Integrable Systems

“表象理论与可积系统”国际会议将于2019年8月12-16日在苏黎世理工大学举行。将有20场知名专家的特邀讲座，年轻教师的贡献演讲，以及一些研究生演讲。会议的目标是研究标题中该领域的最新进展，并教育年轻的研究人员。这一奖项将资助美国科学家参加这次会议，优先考虑最近的博士和未被充分代表的少数族裔，这样他们就可以分享他们的研究，了解该领域的新想法。量子可积系统是作用于向量空间的可交换算符(哈密顿)的大家族。这些族自然而然地出现在约化李代数及其对应的量子群的表示理论中。主要目的是研究哈密顿尼安的光谱。事实证明，这个问题与各种数学理论有着深刻的联系：微分方程式和差分方程式，等变上同调和K-理论，特殊函数理论，组合学等等。这次会议将为不同的研究人员提供一个共同的场所，他们使用不同的方法和不同的目标来研究这一主题，以互动和分享最新的进展。有关这次会议的更多细节，请访问http://rtis2019.math.iupui.edu/，http://www.nccr-swissmap.ch/events/representation-theory-and-integrable-systems.This奖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智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The international conference "Representation theory and integrable systems" will take place at ETH Zurich August 12-16, 2019. There will be twenty invited lectures by renowned experts, contributed talks by younger faculty, and a number of graduate student presentations. The goal of the conference is to study the recent advances in the area in the title and to educate the younger researchers. This award will fund participation of US scientists in this conference, with priority given to recent PhDs and underrepresented minorities, so they can share their research and learn about the new ideas in the field.Quantum integrable systems are large families of commuting operators (Hamiltonians) acting on a vector space. Such families naturally appear in the representation theory of reductive Lie algebras and their corresponding quantum groups. The main goal is to study the spectra of the Hamiltoninians. It turns out that this question has deep connections to various mathematical theories: differential and difference equations, equivariant cohomology and K-theory, the theory of special functions, combinatorics, and more. The conference will provide a common venue for a diverse group of researchers who study the subject using different methods with different goals to interact and share recent advances. More details about the conference are available at http://rtis2019.math.iupui.edu/ and http://www.nccr-swissmap.ch/events/representation-theory-and-integrable-systems.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.