A traditional conference celebrating the collaboration between many institutes in USA, Latin America, Asia and Europe included in the Institute of the Mathematical Sciences of the Americas Consortium (IMSAC). The event is jointly organised by the International Centre for Mathematical Sciences (ICMS‑Sofia) at the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, and the Institute for the Mathematical Sciences of the Americas (IMSA) at the University of Miami.

August 6–7, 2026, Sofia time, ICMS-Sofia hosts a Distinguished Lecture Series in Representation Theory and Mathematical Physics by Quanshui Wu (Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, China) on Equivalence of Quotient Categories, with Applications to Noncommutative Resolutions.

The three lectures take place on August 6 (16:00–17:00) and August 7 (15:00–16:00 and 16:10–17:10). They discuss localization constructions and F-ample generators in abelian categories, applied to establish equivalences of quotient categories and a Morita-type theory for noncommutative resolutions of singularities.

The lectures take place in Room 578, ICMS-Sofia.

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)