Workshop: Real Enumerative Geometry and Beyond; Nashville, TN; March 6-7, 2020

研讨会：实数几何及其他；

• 批准号: 2002974
• 负责人: Rares Rasdeaconu
• 金额: $ 0.9万
• 依托单位: Vanderbilt University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-02-01 至 2022-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2002974&HistoricalAwards=false
• 关键词: Workshop; Real; Enumerative; Geometry; Beyond

This award supports the Shanks workshop “Real Enumerative Geometry and Beyond” that will take place on March 6-7, 2020, at Vanderbilt University, Nashville, TN. The workshop will address the latest advances in the field of mathematics known as the real enumerative geometry, with senior and junior researchers of different expertise reporting on topics of common interests. The main goal of the meeting is to facilitate discussions and collaborations in a focused setting. The small size of the workshop provides an ideal environment for graduate students and early career researchers to interact with experts in the field. A diverse group of researchers will report on new advances in the field, assuring that a vast amount of techniques are shared among its participants. The intensive and substantial exchange of a broad spectrum of ideas during the workshop is expected to stimulate further research with the aim of pushing the boundaries of this field. Real enumerative geometry is an area of research with a long history, which has been rapidly evolving in the recent years. The main impetus in present-day developments comes from ideas of J.-Y. Welschinger, who proposed a signed counting in the enumerative geometry of curves defined over the field of real numbers. These ideas were used to answer many long-standing questions in the enumerative geometry of real algebraic varieties through their implementation in the symplectic, tropical or algebraic geometry framework. Very recently, these ideas were adapted in the A1-homotopy theory in an attempt to answer questions in enumerative geometry over arbitrary fields. The workshop is expected to lift the barriers between the seemingly unrelated fields of real enumerative geometry and A1-homotopy theory and build bridges between these fields. Classical aspects of real enumerative geometry will be addressed by V. Kharlamov, tropical aspects by O. Viro, a symplectic geometry approach will be discussed by X. Chen and S. Tukachinsky, while recent results in A1-enumerative geometry will be presented by J. Kass, S. Pauli and I. Vogt. For more details, see the webpage of the workshop: https://my.vanderbilt.edu/rag2020/ .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.

该奖项支持将于2020年3月6日至7日在田纳西州纳什维尔的范德比尔特大学举行的Shanks研讨会“真实的枚举几何及其他”。讲习班将讨论被称为真实的枚举几何的数学领域的最新进展，不同专业知识的高级和初级研究人员将就共同感兴趣的主题进行报告。会议的主要目标是促进有针对性的讨论和合作。研讨会的小规模为研究生和早期职业研究人员提供了一个理想的环境，与该领域的专家进行互动。一个多元化的研究小组将报告该领域的新进展，确保参与者之间分享大量的技术。讲习班期间广泛深入地交换了各种意见，预计将促进进一步的研究，以扩大这一领域的范围。真实的枚举几何是一个有着悠久历史的研究领域，近年来发展迅速。当今发展的主要动力来自J. Y. Welschinger，他提出了一个有符号的计数在枚举几何的曲线定义的领域的真实的号码。这些想法被用来回答许多长期存在的问题，在枚举几何的真实的代数簇，通过其实施辛，热带或代数几何框架。最近，这些想法被改编成A1-同伦理论，试图回答任意域上的枚举几何问题。该研讨会有望解除真实的枚举几何和A1同伦理论这两个看似无关的领域之间的障碍，并在这些领域之间建立桥梁。真实的枚举几何的经典方面将由V. Kharlamov讨论，热带方面将由O. Viro，辛几何方法将由X. Chen和S. Tukachinsky，而A1-枚举几何的最新结果将由J. Kass，S.保利和我。沃格特。有关更多详细信息，请参阅研讨会的网页：https://my.vanderbilt.edu/rag2020/。该奖项反映了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。