Workshop and Conference: K-theory: Future Directions

“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的俄亥俄州立大学举行。K-理论是研究空间上的向量丛，并提供了空间的非常重要的不变量。根据所考虑的空间和所使用的K-理论的变体，这些不变量对从代数拓扑到数论的数学的不同部分都很重要。因此，该计划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，在过去十年中在该领域取得了重大进展。鉴于这些，研讨会和会议应该是非常感兴趣的初级教师和研究生谁可能开始他们的研究生涯。该计划将以几个主题演讲为特色，这些演讲将调查重点领域的历史背景，发展现状和未来进展前景。这些讲座将提供一个机会，采取比在许多研究会议的习惯更长远的眼光，应该是特别有价值的年轻研究人员。 近年来，在代数K理论领域有几个重大的进展，导致了Milnor，Bloch-Kato和Lichtenbaum-Quillen代数的解决方案。为解决上述问题而采用的强有力的技术促进了对该地区几个悬而未决的问题的研究。研讨会和会议将集中在Koszulity猜想和Carlsson猜想，这是Milnor和Bloch-Kato猜想解决后剩下的主要开放问题之一。这两种说法已经存在了近20年，并且都有特殊的情况得到了验证。从Milnor和Bloch-Kato方程的解来看，这说明了上述研讨会和会议的重要性和现实意义。 有关会议网站，请访问https://people.math.osu.edu/joshua.1/Ktheory_conf.html

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