IRES: USA-Uzbekistan Collaborative Research in Leibniz algebras

美国学生将在一个多元化和充满活力的环境中工作，并与乌兹别克斯坦同行谁是尖端数学研究专家合作。 他们将接触到独特的教学和指导风格，这将丰富他们的学习经验。特别是，该项目将为来自代表性不足群体的妇女和学生提供独特的研究机会。许多加州州立大学和加州大学在南加州的校园，那里的美国学生将被招募，是西班牙裔服务机构和少数民族服务机构。该项目将通过促进两国之间的相互理解而产生社会效益。该项目的目的是让美国学生在著名的乌兹别克数学家Shavkat Ayupov的指导下获得国际研究经验，Shavkat Ayupov是莱布尼茨代数的著名专家。PI将在三年内将三个不同的群体带到乌兹别克斯坦，15至21名美国学生，在乌兹别克斯坦国立大学数学研究所进行为期两个月的研究。美国学生将加入Ayupov的研究小组，并与他们的乌兹别克同行和导师合作，就莱布尼茨代数当前感兴趣的主题进行研究。研究课题的例子包括研究莱布尼兹代数的导子的性质和识别可解刚性莱布尼兹代数。莱布尼茨代数是李代数的推广，是数学中一个重要且快速发展的领域，在广义相对论、量子力学和弦理论中有应用。预计每个研究项目都将产生出版物，并导致进一步的研究合作。除了他们的研究活动，学生还将参加关于乌兹别克斯坦语言，文化和传统的短期课程，以帮助他们适应周围的环境。在乌兹别克斯坦期间，美国学生将前往撒马尔罕、布哈拉和希瓦古城，了解乌兹别克斯坦的文化和科学遗产。

U.S. students will work in a diverse and vibrant environment and collaborate with Uzbek peers who are experts in cutting-edge math research. They will be exposed to unique styles of teaching and mentorship that will enrich their learning experience. In particular, this project will provide unique research opportunities for women and students from under-represented groups. Many of the California State University and the University of California campuses in Southern California, where the U.S. students will be recruited, are Hispanic Serving Institutions and Minority Serving Institutions. The project will have societal benefits by promoting mutual understandings between the two nations. The aim of the project is to give U.S. students international research experiences under the mentorship of a prominent Uzbek mathematician, Shavkat Ayupov, a well-known expert in Leibniz algebras. The PI will take three separate cohorts to Uzbekistan, 15 to 21 U.S. students over three years, to conduct research for two months at the Institute of Mathematics of the National University of Uzbekistan. The U.S. students will join Ayupov's research group and conduct research in collaboration with their Uzbek peers and mentors on topics of current interest in Leibniz algebras. Examples of research topics include studying properties of derivations of Leibniz algebras and identifying solvable rigid Leibniz algebras. The Leibniz algebras, which are generalizations of Lie algebras, are an important and rapidly developing area of mathematics with applications in general relativity, quantum mechanics and string theory. It is expected for each research project to result in publications and lead to further research collaboration. In addition to their research activities, the students will also take short courses on the language, culture and traditions of Uzbekistan to help them adjust to their surroundings. During their stay in Uzbekistan, the U.S. students will travel to the ancient cities of Samarkand, Bukhara and Khiva to learn about the cultural and scientific heritage of Uzbekistan.