RTG: Number Theory and Arithmetic Geometry at Berkeley

RTG：伯克利分校的数论和算术几何

• 批准号: 1646385
• 负责人: Martin Olsson
• 金额: $ 239.72万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-07-15 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1646385&HistoricalAwards=false
• 关键词: RTG; Number; Theory; Arithmetic; Geometry

The Research Training Group (RTG) in Number Theory and Arithmetic Geometry at UC Berkeley will establish a number of activities involving researchers at all career stages ranging from undergraduates to senior faculty. The guiding aim is to create a research group based approach to the training of students and postdocs, enabling them to take full advantage of the wide expertise and experience of each other and the senior faculty, and to provide access for undergraduates to the research of the group and to mentor students planning to pursue related advanced degrees. The RTG will provide a unifying structure for the development of researchers and to foster collaborations. Activities of the RTG include research workshops, new research seminars, undergraduate conferences, and undergraduate mentoring. The research expertise of the faculty affiliated with the RTG covers a wide range of topics in number theory and arithmetic geometry, as well as several related fields such as algebraic geometry, representation theory, and logic. The research conducted as part of this award will include work on automorphic forms, Arakelov geometry, Shimura varieties, Langlands correspondence, p-adic cohomology theories, motives, algebraic dynamics, and log geometry. The project activities will integrate the many research activities of the participants into a coherent research group fostering further collaborations and more extensive training.

加州大学伯克利分校数论和算术几何研究培训小组 (RTG) 将开展一系列活动，涉及从本科生到高级教师等各个职业阶段的研究人员。 指导目标是创建一个基于研究小组的方法来培训学生和博士后，使他们能够充分利用彼此和高级教师的广泛专业知识和经验，并为本科生提供参与研究的机会小组并指导计划攻读相关高级学位的学生。 RTG 将为研究人员的发展和促进合作提供统一的结构。 RTG 的活动包括研究研讨会、新研究研讨会、本科生会议和本科生指导。 RTG 附属教师的研究专业知识涵盖数论和算术几何的广泛主题，以及代数几何、表示论和逻辑等多个相关领域。 作为该奖项的一部分进行的研究将包括自守形式、Arakelov 几何、Shimura 簇、Langlands 对应、p-adic 上同调理论、动机、代数动力学和对数几何等方面的工作。该项目活动将把参与者的许多研究活动整合到一个连贯的研究小组中，促进进一步的合作和更广泛的培训。

项目成果

The Brauer group of the moduli stack of elliptic curves over algebraically closed fields of characteristic 2

特征 2 的代数闭域上椭圆曲线模堆的布劳尔群

• DOI: 10.1016/j.jpaa.2018.08.010
• 发表时间: 2019
• 期刊: Journal of Pure and Applied Algebra
• 影响因子: 0.8
• 作者: Shin, Minseon

The polylog quotient and the Goncharov quotient in computational Chabauty–Kim Theory I

计算 Chabauty 中的多对数商和 Goncharov 商 — Kim 理论 I

• DOI: 10.1142/s1793042120500967
• 发表时间: 2020
• 期刊: International Journal of Number Theory
• 影响因子: 0.7
• 作者: Corwin, David;Dan-Cohen, Ishai
• 通讯作者: Dan-Cohen, Ishai

An Evertse–Ferretti Nevanlinna constant and its consequences

Evertse-Ferretti Nevanlinna 常数及其后果

• DOI: 10.1007/s00605-021-01600-1
• 发表时间: 2021
• 期刊: Monatshefte für Mathematik
• 作者: Ru, Min;Vojta, Paul
• 通讯作者: Vojta, Paul

Projective Geometry for perfectoid spaces

完美空间的射影几何

• DOI: 10.48550/arxiv.1910.05487
• 发表时间: 2021
• 期刊: Munster journal of mathematics
• 作者: Gabriel Dorfsman-Hopkins

Solutions of equations involving the modular $j$ function

涉及模 $j$ 函数的方程的解

• DOI: 10.1090/tran/8244
• 发表时间: 2021
• 期刊: Transactions of the American Mathematical Society
• 影响因子: 1.3
• 作者: Eterović, Sebastian;Herrero, Sebastián
• 通讯作者: Herrero, Sebastián