Conference: Workshop in Commutative Algebra

这笔赠款为美国的研究人员提供资金，让他们参加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。会议的焦点将是素数特征和混合特征的交换代数和代数几何，这是近些年来取得惊人进展的纯数学领域。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。这笔资金的支持将使来自美国的科学家有机会参加会议，并与一批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，随着紧闭包理论在20世纪80年代的创立，素数特征的交换代数和代数几何已经成为一个重要的和充满活力的数学领域。它带来了巨大的改进，并对许多结果进行了更简单的证明。它还提供了奇点的概念，这些奇点是纯代数定义的，但有点神秘地对应于复数领域中的二元几何中出现的奇点类型。混合特征交换代数是对不包含任何域的环的研究，通过最近著名的同调猜想的解决，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早期职业数学家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。这所科学学院的网站是https://indico.ictp.it/event/10200.研讨会的网站是https://indico.ictp.it/event/10276.This奖，反映了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 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.