This article is about naturally occurring objects in computability theory, the area inside mathematical logic that studies the complexity of infinite countable objects. Martin’s conjecture is currently one of the main open questions in computability theory and is of great foundational importance.
Connes’ embedding problem asks if every type II$_1$ factor acting on a separable Hilbert space is embeddable into an ultrapower of the hyperfinite II$_1$ factor via a nonprinciple ultrafilter. Roy Araiza and Rolando de Santiago unravel the meaning behind Connes’ embedding problem and highlight its significance.
While invariants of geometric or topological objects can be of any sort, most modern invariants are algebraic in nature. The goal of this article is to survey some of the ways in which categorical algebra can be utilized to measure topological phenomena.
One of the greatest strengths of the AMS is its vibrant community. In an effort to help our readers easily find possibilities for personal, academic, and career enhancement and development, we make this comprehensive list (updated regularly) available. From Fellowships and Calls for Nomination to Membership Benefits and open positions, this is your gateway to involvement and engagement opportunities with the AMS. View the List
A new community project for 2019, these thematic-compilations of articles inform graduate students, job seekers, early career academics, and mentors.
This section features positions on all Society policy, reports on governance and committee activities, and maintains institutional memory.
A new section for 2019 whose articles discuss and highlight reports, surveys, trends, and the pivotal role education plays in STEM.
Math Societies to Lawmakers: Help Us Make the Master Key
Showcasing important mathematical discoveries that have taken place in national laboratories and agencies.
One Spark Is All You Need: Germain Gets the Hamilton Treatment
The Notices Classified Advertising section is devoted to listings of current employment opportunities
This news section highlights AMS announcements and offers readers a snapshot of current AMS opportunities
We invite readers to submit letters to the editor to Notices at
A link to the AMS Math Calendar, an interactive page where readers can submit or search international math events and meetings
Opportunities to apply for fellowships and grants, to nominate colleagues for prizes and awards, and to submit proposals for meetings and workshops
Profiles of recent newsmakers in the math community
A listing of sectional, national, and international meetings held and/or hosted by the AMS
Notifications and descriptions of new AMS publications