# Overview

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The representation theory of Lie algebras, quantum groups and algebraic groups represents a major area of mathematical research in the twenty-first century with numerous applications in other areas of mathematics (geometry, number theory, combinatorics, finite and infinite groups,) and mathematical physics (conformal field theory, statistical mechanics, integrable systems). There are various approaches to study representation theory and this workshop will focus on the algebraic and combinatorial approaches to the subject. The representation theory of quantized enveloping algebras, Kac-Moody Lie algebras, extended affine Lie algebras and Hecke algebras involves many ideas which have been developed for algebraic groups and Lie groups. The full impact of the interplay between algebraic groups, quantum groups and Kac-Moody Lie groups is yet to be realized and one of the aims of the workshop is to bring together specialists in these areas to explore this in more depth. The combinatorial aspects of the conference will revolve around the theory of canonical bases and crystal bases introduced and studied by Lusztig and Kashiwara. The connections of the subject with the theory of solvable lattice models will also be a theme of the conference.