A glimpse into geometric representation theory : virtual AMS Special Session on Combinatorial and Geometric Representation Theory, 2022 / edited by Mahir Bilen Can and Jörg Feldvoss.

Includes bibliographical references.

Includes articles on motivic Chern classes, Lie superalgebras, Nash manifolds, Macdonald polynomials, and meromorphic connections.

This volume brings together a collection of advanced research and survey papers presented at a virtual AMS Special Session devoted to combinatorial and geometric representation theory. The contributions reflect the growing synthesis of algebraic, geometric, and combinatorial perspectives in modern mathematical research, illustrating how geometric intuition and structures can be used to understand and classify representations of algebraic objects. The articles explore a broad spectrum of interconnected themes, including equivariant characteristic classes and their applications in geometry, representation theory of Lie algebras and Lie superalgebras, and the role of combinatorial structures such as partitions, tableaux, and symmetric functions in encoding representation-theoretic data. Several papers investigate geometric methods in representation theory, such as the use of algebraic varieties, flag varieties, and Nash manifolds, highlighting how geometric spaces provide a natural setting for studying symmetries and invariants. Further contributions address specialized topics like Macdonald polynomials, categorification, and connections with algebraic combinatorics, as well as the study of meromorphic connections and moduli spaces on algebraic curves. These works demonstrate the deep interplay between local and global geometric structures and their influence on representation-theoretic phenomena. Overall, the volume offers both a snapshot of current research trends and a conceptual framework for understanding ongoing developments in geometric representation theory. It serves as a valuable resource for researchers, advanced students, and specialists seeking insight into the unifying methods and emerging directions at the intersection of algebra, geometry, and combinatorics.