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

该奖项支持将于2020年3月6-7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“实数几何及以后”。研讨会将讨论被称为真正的计数几何的数学领域的最新进展，不同专业的高级和初级研究人员将就共同感兴趣的主题进行报告。会议的主要目标是在有重点的情况下促进讨论和合作。研讨会的面积很小，为研究生和早期职业研究人员与该领域的专家互动提供了理想的环境。一组不同的研究人员将报告该领域的新进展，确保参与者分享大量技术。讲习班期间密集和实质性的广泛思想交流预计将促进进一步的研究，目的是推动这一领域的边界。实数几何是一个历史悠久的研究领域，近年来得到了迅速的发展。当今发展的主要推动力来自J.-Y.Welschinger的想法，他提出了实数域上定义的曲线的计数几何中的符号计数。这些思想通过在辛几何、热带几何或代数几何框架中的实现，被用来回答实代数簇的计数几何中的许多长期存在的问题。最近，这些想法被应用到A1-同伦理论中，试图回答任意域上的计数几何中的问题。研讨会有望消除实数列几何和A1-同伦理论这两个看似不相关的领域之间的障碍，并在这些领域之间架起桥梁。实数列几何的经典方面将由V.Kharlamov讨论，热带方面将由O.Viro讨论，辛几何方法将由X.Chen和S.Tukachinsky讨论，而A1-计数几何的最新结果将由J.Kass，S.Pauli和I.Vogt给出。更多详情，请访问研讨会的网页：https://my.vanderbilt.edu/rag2020/。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智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.