54 | XX REPRESENTATION THEORY

Lie Groups Section: the topic of this section is Representations of reductive Lie groups, and their algebraic analogs, the Harish-Chandra modules. The talks will address various issues about the invariants of representations and Harish-Chandra modules, questions related to unitarity, connections to various kinds of geometry, and other applications.
The Vertex Algebra section of Representation Theory XX will highlight recent advances at the interface of vertex algebra theory and representation theory. Topics will include vertex algebras associated with infinite-dimensional Lie algebras and superalgebras, W-algebras, logarithmic vertex algebras, vertex algebras arising from the 4d/2d correspondence, and quantum vertex algebras. The section aims to bring together researchers working on algebraic and combinatorial aspects of vertex algebra theory, while also presenting new connections between this field and theoretical physics. The conference will foster discussions among leading experts and encourage the development of new collaborations.
The Number Theory section of Representation Theory XX will feature recent advances at the interface of number theory and representation theory. Topics include arithmetic aspects of elliptic curves and abelian varieties, Diophantine equations and tuples, properties of algebraic number fields, and problems related to modular forms and p-adic methods. The program will also highlight connections with arithmetic geometry, computational approaches, and emerging data-driven techniques. The section aims to bring together researchers working on both classical and modern problems, fostering interaction between different perspectives and encouraging new collaborations.