New Directions in Iwasawa Theory (16w5043)
Frauke Bleher (University of Iowa)
Ted Chinburg (University of Pennsylvania)
Ralph Greenberg (University of Washington)
Georgios Pappas (Michigan State University)
Romyar Sharifi (University of Arizona)
A main goal of this workshop is to prepare the ground for anticipated significant scientific developments in the mathematical sciences. Iwasawa theory is undergoing rapid change in several directions. One goal of the workshop will be to map out some primary new objectives for Iwasawa theory over the next ten years.
This workshop will bring together researchers and advanced Ph.D. students working on Iwasawa theory and related topics in K-theory, commutative algebra and modular forms in order to further advance these fields. A specific objective of the workshop will be to discuss recent advances in Iwasawa theory, as discussed in the section of the proposal concerning the subject area of the workshop. Another objective is the development of deeper ties between Iwasawa theory and algebraic K-theory.
It will bring together researchers with a wide range of expertise in number theory, algebraic K-theory, homological algebra and arithmetic geometry. It will also introduce young researchers and members of underrepresented groups to previous work as well as new directions for research in these areas. A workshop about Iwasawa theory is timely in view of the recent proofs of a number of Main Conjectures about first Chern classes. These include the non-commutative Main Conjecture over totally real fields in 2010, the final form of the commutative Main Conjecture over imaginary quadratic fields in 2011, and recent progress on Main Conjectures relating to modular forms.
It is appropriate to have this workshop in 2016 because the organizers (Bleher, Chinburg, Greenberg, Pappas and Sharifi) are currently P.I.'s on a Focused Research Group award from the N.S.F. concerning Iwasawa theory and Chern classes. Two consultants on the FRG grant are Mahesh Kakde and Martin J. Taylor. This N.S.F. FRG project includes as one goal organizing a conference on Iwasawa theory in 2016.