Expanding representation in Noncommutative Algebra and Representation Theory: WINART2 Workshop

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

This award supports the participation of underrepresented minorities in the Women in Noncommutative Algebra and Representation Theory workshop (WINART2) at the University of Leeds on May 20 - 24, 2019. Noncommutative algebra and representation theory are two closely intertwined areas of research in Algebra that have strong ties to many other fields in mathematics and quantum physics such as conformal field theory, operator algebras, string theory, topological field theory, and the various guises of noncommutative geometry. Noncommutative algebra creates an algebraic framework for generalizing the study of polynomials to other rings that fail to be commutative, and representation theory is a powerful tool for investigating the action of an algebraic object on a space as linear operators and matrices. As in many areas of mathematics, women have been underrepresented in these areas of research. The goal of this workshop to bring together some of the best experts and junior participants working on these topics, particularly researchers from underrepresented groups, to collaborate on research projects. This workshop will be the second of its kind for these fields. Like the first WINART workshop (held at BIRS in March 2016), WINART2 will have a great impact on the research careers of those in attendance, and as a result, it will positively impact the research area as a whole. Funding will be prioritized for US-based junior participants. There will be eight research groups present at the workshop led by a pair of research leaders in Noncommutative Algebra and Representation Theory. Topics include: cluster categories; tensor invariants under Hopf algebra actions; algebraic, geometric, and categorical aspects of diagram algebras; Brauer and partition algebras; geometric models and representation theory; Burnside rings and Mackey functors for profinite groups; quantum symmetries- fusion categories and Hopf algebras; and Hochschild (co)homology, quivers and Gerstenhaber bracket. Further information can be found at the workshop website: http://women-in-ncalg-repthy.org/conferences/winart2-workshop-may-2019/. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.