2020 - 2022 Talbot Workshops on Mathematics Centering on Algebraic Topology

该奖项为将于6月21日至27日在德克萨斯州纳科多奇斯举行的2020年Talbot研讨会“色同伦理论中的双灵巧性”以及2021年和2022年的后续研讨会提供支持。这些研讨会的结构反映了这样一个事实，即数学是一项强烈的合作努力，需要几代人之间的指导，并在给定的队列中形成信任关系。自2004年首次会议以来，Talbot研讨会采用了一种独特的以人为中心的方法，在以代数拓扑为中心的广泛数学领域中，向数十名年轻研究人员介绍了当代感兴趣的主题。每个工作坊约有35名青年参加者和一至两名资深数学家参加，为期一周。参与者多为研究生，在导师的指导下，通过交流讲座和讨论，了解工作坊的研究课题。由于许多参与者都是一年级或二年级的研究生，希望在一个有前途的研究领域开始，因此讲座以基本的介绍性材料开始，并引导到开放性问题的展示。研讨会非常成功，激发了许多学生未来的研究，并在参与者之间建立了许多合作。我们将继续认真努力，确保有广泛和多样化的参与者名单。工作坊的独特形式是参与者在出租的房子里一起生活和做饭，这有助于创造和维持一种轻松和合作的氛围。组织研讨会为领导委员会的专业发展提供了一个重要的机会，该委员会完全由研究生组成，并由一名资深教员负责监督。过去的Talbot研讨会专注于同伦理论及其周边领域的各种主题，从椭圆上同调（2004年）和Fukaya范畴（2009年）到非阿贝尔Hodge理论（2011年）和Kervaire不变量问题的解决（2016年），以及最近流形的模空间的最新进展（2019年）。2020年研讨会的主题是“色同伦理论中的双灵巧性”。它将由雅各布·卢里（普林斯顿大学高级研究所）和托默·施兰克（耶路撒冷希伯来大学）指导。塔尔博特研讨会的网站是http://math.mit.edu/conferences/talbot/.This，该奖项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知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This award provides support for the 2020 Talbot Workshop "Ambidexterity in Chromatic Homotopy Theory" to be held June 21-27 in Nacogdoches, TX, as well as for subsequent workshops in 2021 and 2022. The structure of these workshops reflects the fact that mathematics is an intensely collaborative endeavor, requiring mentorship across generations and formation of trusting relationships within a given cohort. Since the initial meeting, in 2004, the Talbot Workshops have employed a uniquely human-centered approach in introducing scores of young researchers to topics of contemporary interest in a broad range of mathematics centering on algebraic topology. Each workshop gathers about 35 young participants and one or two senior mathematicians for a week-long retreat. The participants, who are mostly graduate students, learn about the workshop’s research topic by exchanging lectures and discussing the topic under the guidance of the mentors. As many of the participants are first- or second-year graduate students looking to get a start in a promising research area, the lectures begin with basic introductory material and lead up to a presentation of open problems. The workshop has been extremely successful, inspiring the future research of many students and establishing numerous collaborations among the participants. There will continue to be a serious effort to insure a broad and diverse participant list. The workshop’s unique format, in which participants live and cook together in a rental house, helps to create and sustain a relaxed and collaborative atmosphere. Organizing the workshop provides an important opportunity for professional development by the leadership committee, which is entirely made up of graduate students with backup oversight by a senior faculty member.Past Talbot Workshops have focused on a wide variety of topics in homotopy theory and surrounding areas, from elliptic cohomology (2004) and Fukaya categories (2009) to non-abelian Hodge theory (2011) and solution of the Kervaire invariant problem (2016), and most recently, recent progress on Moduli Spaces of Manifolds (2019). The topic for the 2020 workshop is "Ambidexterity in Chromatic Homotopy Theory." It will be mentored by Jacob Lurie (Institute for Advanced Study, Princeton) and Tomer Schlank (Hebrew University, Jerusalem). The web site for the Talbot workshops is http://math.mit.edu/conferences/talbot/.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.