Conference: Workshop in Commutative Algebra

这项资助为美国科学家提供资金，让他们参加将于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）举行的为期两周的科学学校和研讨会。会议的重点将是交换代数和代数几何中的质数特征和混合特征，这是近年来取得惊人进展的纯数学领域。ICTP的重点是支持发展中国家的先进研究和科学研究。这项资助的支持将使来自美国的科学家有机会参加这次会议，并与来自发展中国家的一组研究人员以及该领域的其他主要国际专家进行互动和合作。更详细地说，随着20世纪80年代紧闭理论的出现，交换代数和素数特征代数几何成为数学中一个重要而充满活力的领域。它带来了巨大的改进，并简化了许多结果的证明。它还提供了奇点的概念，这些概念是纯代数定义的，但有点神秘地对应于在复数域上出现的两族几何中的奇点类型。混合特征中的交换代数，即不包含任何场的环的研究，通过最近著名的同调猜想的解，已经看到了新方法的引入和惊人的进展。ICTP的科学学院和研讨会将为学生提供早期职业数学家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。科学学校的网站是https://indico.ictp.it/event/10200。研讨会的网站是https://indico.ictp.it/event/10276.This，该奖项反映了NSF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 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.