Representation Theory and Integrable Systems

国际会议“表示理论和可积系统”将于2019年8月12日至16日在ETH苏黎世举行。将有二十个著名专家的邀请讲座，由年轻的教师贡献的会谈，和一些研究生的演讲。会议的目的是研究该领域的最新进展，并教育年轻的研究人员。该奖项将资助美国科学家参加本次会议，优先考虑最近的博士和代表性不足的少数民族，这样他们就可以分享他们的研究和了解该领域的新思想。量子可积系统是作用于向量空间的交换算子（哈密顿算子）的大家族。这样的族自然地出现在约化李代数及其相应的量子群的表示论中。主要目的是研究哈密顿量的谱。事实证明，这个问题与各种数学理论有着深刻的联系：微分方程和差分方程，等变上同调和K理论，特殊函数理论，组合学等等。该会议将为研究该主题的不同研究人员提供一个共同的场所，他们使用不同的方法与不同的目标进行互动并分享最新进展。有关会议的更多细节可在http://rtis2019.math.iupui.edu/和http://www.nccr-swissmap.ch/events/representation-theory-and-integrable-systems.This奖项反映了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。

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.