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理论是对空间上的向量捆绑包的研究，并提供了该空间非常重要的不变性。根据所考虑的空间和所使用的K理论的变体，这些不变性对于数学的不同部分至关重要，从代数拓扑到数字理论。结果，程序主题在于代数拓扑，代数几何和算术几何形状中非常活跃的地区的交集，在过去的十年中，该地区取得了重大进展。鉴于这些，研讨会和会议应该引起可能开始研究职业的初级教师和研究生。该计划将进行几个钥匙主说话，这些谈判将调查历史背景，当前的发展状态以及在集中领域的未来进步的前景。这些谈判将为您提供比许多研究会议的习惯，对年轻研究人员特别有价值。 近年来，代数K理论领域取得了一些重大进步，导致了Milnor，Bloch-Kato和Lichtebaum-Quillen猜想的解决方案。用于解决上述猜想的解决方案引入的强大技术激发了该地区几个出色的剩余问题的工作。研讨会和会议将重点介绍Koszulity的猜想和卡尔森猜想，这是Milnor和Bloch-Kato猜想解决方案后的主要剩余问题之一。这两个猜想已经存在了近20年，并且已经验证了两者的特殊情况。鉴于Milnor和Bloch-Kato的解决方案，这表明了上述研讨会和会议的重要性和相关性。 有关会议网站，请访问https://people.math.osu.edu/joshua.1/ktheory_conf.html