Conference: Workshop in Commutative Algebra

这笔赠款为美国的研究人员提供资金，参加为期两周的科学学校和研讨会，将于2023年5月2日至12日在意大利的里雅斯特国际理论物理中心（ICTP）举行。会议的重点将是交换代数和代数几何的主要特征和混合特征，纯数学的一个领域，近年来取得了巨大的进展。国际理论物理中心的重点是支持发展中国家的高级研究和科学研究。来自该基金的支持将使美国的科学家有机会参加会议，并与来自发展中国家的研究人员以及该领域的其他领先国际专家进行互动和合作。更详细地说，随着20世纪80年代紧闭理论的诞生，交换代数和素特征代数几何已成为数学中一个重要而又充满活力的领域。它导致了大量的改进和许多结果的简单证明。它还提供了奇点的概念，这些奇点是纯粹用代数定义的，但有点神秘地对应于复数域上双有理几何中出现的奇点类型。混合特征的交换代数，研究不包含任何域的环，通过最近解决著名的同调代数，已经看到了新方法的引入和惊人的进展。国际理论物理中心的科学学校和研讨会将为早期职业数学家的学生提供参与这些快速发展领域的机会，更有经验的研究人员将有机会发起新的跨国合作。科学学院的网站是https://indico.ictp.it/event/10200。该研讨会的网站是https://indico.ictp.it/event/10276.This奖反映了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。

This grant provides funding for US-based researchers to participate in a two-week long scientific school and workshop that will take place May 2-12, 2023 at the International Centre for Theoretical Physics (ICTP) in Trieste, Italy. The focus of the meeting will be commutative algebra and algebraic geometry in prime characteristic and mixed characteristic, an area of pure mathematics that has seen fantastic advances in recent years. The ICTP is focused on supporting advanced studies and scientific research in developing countries. Support from this grant will give scientists from the US the opportunity to participate in the meeting and to interact and collaborate with a cohort of researchers from the developing world, as well as other leading international experts in the field.In more detail, with the inception of tight closure theory in the 1980s, commutative algebra and algebraic geometry in prime characteristic has become an important and vibrant field of mathematics. It has lead to vast improvements and simpler proofs of many results. It has also provided notions of singularities that are defined purely algebraically but correspond, somewhat mysteriously, to types of singularities that appear in birational geometry over the field of complex numbers. Commutative algebra in mixed characteristic, the study of rings that do not contain any field, has seen the introduction of new methods and spectacular advances through the recent solution of the celebrated homological conjectures. The scientific school and workshop at ICTP will give students early-career mathematicians an opportunity to get involved in these fast moving areas, and more experienced researchers will have a chance to initiate new trans-national collaborations. The website for the scientific school is https://indico.ictp.it/event/10200. The website for the workshop is https://indico.ictp.it/event/10276.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.