The conference brings together leading senior researchers and promising early-career scholars working in the field of Geometry to popularise recent developments and new achievements. It also seeks to give young scholars from South-Eastern Europe the opportunity to engage with cutting-edge research and meet leading experts from around the world.

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 algebraic varieties and reveal properties of them through combinatorial rules. Cluster algebras are essential in the study of canonical bases in diverse settings.

Organizers:

• Milen Yakimov (ICMS – Sofia & Northeastern University)
• Emine Yıldırım (ICMS – Sofia)

August 17–21, 2026, 16:00–17:00 Sofia time, ICMS-Sofia hosts a Distinguished Lecture Series in Representation Theory and Mathematical Physics by Chelsea Walton (Rice University, Houston, USA) on A Century of Frobenius Algebras, based on the speaker’s book in preparation, Symmetries of Algebras, Volume 2.

The five lectures cover: (1) classical Frobenius algebras; (2) monoidal category preliminaries; (3) algebraic structures in monoidal categories; (4) connections to 2-dimensional Topological Quantum Field Theories; (5) representations and functorial constructions.

The lectures take place in Room 403, ICMS-Sofia.

An international conference bringing together leading researchers in Hodge theory and birational geometry, mixing a main conference programme with four confirmed mini-courses by Benjamin Bakker, Leonardo Cavenaghi, Bruno Klingler and Claire Voisin.