Workshop and Conference: K-theory: Future Directions

研讨会和会议：K 理论：未来方向

• 批准号: 1519043
• 负责人: Roy Joshua
• 金额: $ 3.4万
• 依托单位: Ohio State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-03-01 至 2017-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1519043&HistoricalAwards=false
• 关键词: Workshop; Conference; theory; Future; Directions

The "K-theory: Future Directions" workshop/conference will be held at the Ohio State University, Columbus, Ohio, May 11-16, 2015. K-theory is the study of vector bundles on spaces and provides very important invariants of the space. Depending on the space considered and the variant of K-theory used, these invariants are of importance to different parts of mathematics ranging from algebraic topology to number theory. As a result, the program theme lies in the intersection of very active areas in algebraic topology, algebraic geometry and arithmetic geometry,with major advances made in the area during the last decade. In view of these, the workshop and conference should be of great interest to junior faculty and graduate students who may be starting their research careers. The program will feature several key-note talks which will survey the historical background, current state of development and prospects for future progress in the focused areas. These talks will provide an opportunity to take a longer view than is customary at many research conferences and should be particularly valuable for young researchers. In recent years, there have been several major advances in the field of Algebraic K-theory, leading up to the solution of the Milnor, Bloch-Kato and Lichtenbaum-Quillen conjectures. The powerful techniques introduced for the solution of the above conjectures have stimulated work on several outstanding remaining problems in the area. The workshop and conference will focus on the Koszulity conjecture and the Carlsson conjecture, which are among the main remaining open problems after the solution of the Milnor and Bloch-Kato conjectures. The two conjectures have been around for nearly 20 years and special cases of both have been verified. In view of the solution of the Milnor and Bloch-Kato conjectures, this shows the importance and relevance of the above workshop and conference. For the conference web-site, please visit https://people.math.osu.edu/joshua.1/Ktheory_conf.html

“K 理论：未来方向”研讨会/会议将于 2015 年 5 月 11 日至 16 日在俄亥俄州哥伦布市俄亥俄州立大学举行。K 理论是对空间向量丛的研究，并提供了非常重要的不变量空间。根据所考虑的空间和所使用的 K 理论的变体，这些不变量对于从代数拓扑到数论的不同数学部分都很重要。因此，该项目的主题在于代数拓扑、代数几何和算术几何中非常活跃的领域的交叉点，并且在过去十年中该领域取得了重大进展。鉴于这些，研讨会和会议应该引起可能开始其研究生涯的初级教师和研究生的极大兴趣。该计划将包括几场主题演讲，将探讨重点领域的历史背景、发展现状和未来进展前景。这些演讲将提供一个比许多研究会议惯例更长远的机会，对年轻研究人员来说尤其有价值。 近年来，代数 K 理论领域取得了几项重大进展，导致了 Milnor、Bloch-Kato 和 Lichtenbaum-Quillen 猜想的解决。为解决上述猜想而引入的强大技术刺激了对该领域几个悬而未决的问题的研究。本次研讨会和会议将重点讨论科苏利蒂猜想和卡尔森猜想，它们是米尔诺猜想和布洛赫-加藤猜想解决后剩下的主要悬而未决的问题之一。这两个猜想已经存在了近20年，并且两者的特殊情况都得到了验证。鉴于Milnor和Bloch-Kato猜想的解决，这表明了上述研讨会和会议的重要性和现实意义。 会议网站请访问https://people.math.osu.edu/joshua.1/Ktheory_conf.html