Moduli Spaces and Vector Bundles, New trends

模空间和向量丛，新趋势

• 批准号: 2203287
• 负责人: Montserrat Teixidor-i-Bigas
• 金额: $ 1.36万
• 依托单位: Tufts University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-06-01 至 2024-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2203287&HistoricalAwards=false
• 关键词: Moduli; Spaces; Vector; Bundles; New

The grant will provide support for several early-career mathematicians based in the US to attend a five-day international conference, "Moduli Spaces and Vector Bundles, New Trends", to be held at the University of Warwick, U.K. The study of moduli spaces for curves and vector bundles continues to be at the forefront of Algebraic Geometry, and this conference will present recent developments of the theory of moduli spaces and explore further open questions. The award will allow the early-career mathematicians to attend lectures, present in poster sessions, discuss questions with experts in the field, and receive advice and mentorship that will enhance the ability to continue their work. The organizers of the conference have a track record of promoting diversity and encouraging the incorporation of new talent into the field, and women and members of under-represented minorities will be encouraged to participate. For more information, see the conference page http://vbac.wikidot.com/vbac2022.The main topic of the conference will be moduli theory and applications with an emphasis on questions related to vector bundles. One focus will be general theory of stability conditions in derived categories. The theory of Bridgeland stability has matured to provide a powerful tool to study classical problems in algebraic geometry and to analyze moduli spaces of sheaves. A second focus is non-reductive geometric invariant theory, which can be used to construct moduli spaces that include unstable objects or involve non-reductive group actions; important work on the cohomology of such quotients is in progress. Next, higher rank Brill–Noether theory, an ongoing enterprise, has already born some fruit in applications such as computing the Kodaira dimension of spaces of Pryms. The final subtopics, moduli of Higgs bundles and character varieties, are related via the non-abelian Hodge Theorem. World experts in these fields will participate in the conference and present their latest results. Discussions taking place during the conference are likely to lead to further progress in the field. This award will allow US scholars to travel to the UK to attend this impactful event. For more information, see the conference page http://vbac.wikidot.com/vbac2022.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.

该笔拨款将资助数位在美国工作的早期数学家参加在英国沃里克大学举行的为期五天的国际会议，名为“模空间和向量束，新趋势”。 曲线和向量丛的模空间的研究仍然是代数几何的前沿，本次会议将介绍模空间理论的最新发展，并探讨进一步的开放问题。该奖项将允许早期职业数学家参加讲座，在海报会议上展示，与该领域的专家讨论问题，并获得建议和指导，以提高继续工作的能力。会议的组织者在促进多样性和鼓励新人才进入该领域方面有着良好的记录，将鼓励妇女和代表性不足的少数群体成员参加。欲了解更多信息，请参阅会议页面http://vbac.wikidot.com/vbac2022.The会议的主题将是模理论和应用，重点是与向量束相关的问题。一个重点将是一般理论的稳定性条件在派生类别。Bridgeland稳定性理论的成熟为研究代数几何中的经典问题和分析层的模空间提供了有力的工具。 第二个重点是非约化几何不变理论，它可以用来构造包含不稳定对象或涉及非约化群作用的模空间;关于这种不稳定性的上同调的重要工作正在进行中。 其次，高阶Brill-Noether理论，一个正在进行的事业，已经在计算Pryms空间的科代拉维等应用中取得了一些成果。 最后的副主题，模的希格斯束和字符品种，通过非阿贝尔霍奇定理。 这些领域的世界专家将参加会议并介绍他们的最新成果。会议期间进行的讨论很可能导致在该领域取得进一步进展。该奖项将允许美国学者前往英国参加这一有影响力的活动。 欲了解更多信息，请参阅会议页面http://vbac.wikidot.com/vbac2022.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。