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11-16日在俄亥俄州哥伦布市的俄亥俄州立大学举行。k理论是对空间上向量束的研究，它提供了空间中非常重要的不变量。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不同数学部分都很重要。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集，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。该计划将以几场主题演讲为特色，探讨重点领域的历史背景、发展现状和未来进展前景。这些会谈将提供一个机会，比许多研究会议上的惯例更长远地看待问题，对年轻的研究人员尤其有价值。近年来，代数k理论领域取得了几项重大进展，导致了Milnor猜想、Bloch-Kato猜想和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该领域若干悬而未决的问题的研究。研讨会和会议将集中讨论Koszulity猜想和Carlsson猜想，这是在Milnor猜想和Bloch-Kato猜想解决后仍然存在的主要开放性问题。这两种猜想已经存在了近20年，它们的特殊情况都得到了证实。鉴于米尔诺猜想和布洛赫-加托猜想的解决，这显示了上述讲习班和会议的重要性和相关性。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