Workshop and Conference: K-theory: Future Directions

Ohio State University, The, Columbus OH

Investigators

Abstract

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