August 21, 2016

Conference Will Tackle Open Problems in Universal Algebra

What are the most interesting and promising open problems in the field of universal algebra? Answering that question and beginning work on them is the goal of a two-week conference entitled “Structure and Complexity in Universal Algebra,” which will take place at Vanderbilt University September 19-30, 2016.

Universal algebra is the study of algebraic structures, where an algebraic structure is a set together with a collection of operations on that set. Algebraic structures include lattices, groups, rings, and fields. The conference will focus on problems in this area that are “ripe for a definitive breakthrough,” according to Vanderbilt Department of Mathematics Distinguished Professor Ralph McKenzie. McKenzie, who was named a Fellow of the American Mathematical Society in 2015 for his contributions to universal algebra, is organizing the conference together with his former postdoc Matthew Moore.

The conference is structured as a workshop in which researchers will first meet together to identify the problems to be addressed, then break into small groups to work on them. Participants will include mathematicians from eight countries who are working on open problems in universal algebra.

Funding for the event is partly provided by a five-university research grant from the National Science Foundation that aims specifically at achieving advances in these problems. The five universities are home to senior and young mathematicians who are already working together on them. The grant proposal contains details of recent progress on some of the most significant problems.

All of the senior researchers involved in the grant will be attending the workshop. In addition to McKenzie, they are: Clifford Bergaman of Iowa State University, Ralph Freese of the University of Hawaii, Keith Kearnes and Agnes Szendrei of the University of Colorado at Boulder, and George McNulty from the University of South Carolina at Columbia. Most of the younger mathematicians who are working with them will be participants as well.

More information about the “Structure and Complexity in Universal Algebra” conference is available on the conference web site.