Proceedings from a virtual AMS Special Session reveal exciting progress in geometric representation theory, showcasing how geometric methods inform fresh algebraic insights. Articles examine topics including equivariant classes, semialgebraic spaces, Nash manifolds, Lie superalgebras, and wreath Macdonald polynomials.
This volume contains the proceedings of the AMS Special Session on Combinatorial and Geometric Representation Theory, held virtually on November 20-21, 2021. The articles offer an engaging look into recent advancements in geometric representation theory.

Despite diverse subject matters, a common thread uniting the articles of this volume is the power of geometric methods. The authors explore the following five contemporary topics in geometric representation theory: equivariant motivic Chern classes; equivariant Hirzebruch classes and equivariant Chern-Schwartz-MacPherson classes of Schubert cells; locally semialgebraic spaces, Nash manifolds, and their superspace counterparts; support varieties of Lie superalgebras; wreath Macdonald polynomials; and equivariant extensions and solutions of the Deligne-Simpson problem.

Each article provides a well-structured overview of its topic, highlighting the emerging theories developed by the authors and their colleagues.