An ideal illustration of how modern techniques in arithmetic geometry can be fruitfully combined with class field theory to answer concrete questions about abelian varieties.
The Role of Copyright in a Digital Era
In his latest Scholarly Kitchen blog post, AMS Associate Executive Director, Publishing Robert Harington considers the role of copyright and the rise of the Copyright Clearance Center (CCC).
AMS President Vogan's Response Regarding "Middle East" Article in Notices
"The November 2013 issue of the Notices of the American Mathematical Society carried an article "Principles for implementing a potential solution to the Middle East conflict," by Thomas L. Saaty and H. J. Zoffer. A number of you have written to me to express the belief that the article is entirely political in character, and therefore inappropriate for the Notices. The first thing to say is that the conclusions of the article do not represent positions of the American Mathematical Society. So why was the article published?" ...Read More...
Cluster algebras: an introduction
Cluster algebras are commutative rings with a set of distinguished generators having a remarkable combinatorial structure. They were introduced by Fomin and Zelevinsky in 2000 in the context of Lie theory, but have since appeared in many other contexts, from Poisson geometry to triangulations of surfaces and Teichmüller theory. In this expository paper we give an introduction to cluster algebras, and illustrate how this framework naturally arises in Teichmüller theory. We then sketch how the theory of cluster algebras led to a proof of the Zamolodchikov periodicity conjecture in mathematical physics.