The International Center for Mathematical Sciences – Sofia (ICMS-Sofia) hosts an international conference on Quantum Groups and Cluster Algebras between 15-19 December 2025 at the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences. The aim of this conference is to bring together researchers to share recent advances, promote further developments in the theory of Quantum Groups and Cluster Algebras, and to investigate their interactions and applications across mathematics and physics. Quantum groups and cluster algebras both provide frameworks for encoding algebraic and geometric structures arising in representation theory, geometry, and mathematical physics. Quantum groups, as deformations of universal enveloping algebras, capture generalized symmetries with rich categorical and representation-theoretic properties. On the other hand, Cluster algebras, introduced by Fomin and Zelevinsky, appear as important [...]