The group working in Quantum Groups and Cluster Algebras focuses on several major lines of projects addressing key open problems in the two areas. The group seeks to understand the structure of finite tensor categories and their stable triangulated categories. The group investigates the properties of braided tensor categories and their module categories, and on the algebra level, the structure of quasitriangular comodule algebras and coideal subalgebras of quasitriangular Hopf algebras. The group works on the construction of quantum cluster algebra structures on the quantized coordinate rings of important varieties in Lie theory.
Research plan
The group working in Quantum Groups and Cluster Algebras focuses on several major lines of projects addressing key open problems in the two areas. The group seeks to understand the structure of finite tensor categories and their stable triangulated categories. The group investigates the properties of braided tensor categories and their module categories, and on the algebra level, the structure of quasitriangular comodule algebras and coideal subalgebras of quasitriangular Hopf algebras. This has important applications to topological quantum field theory and quantum symmetric spaces.
The group works on the construction of quantum cluster algebra structures on the quantized coordinate rings of important varieties in Lie theory. This gives powerful tools for the study of the canonical bases of the latter and the representations of quantum affine algebras via methods from cluster algebras. Quantum and classical freezes are studied via tools from Calabi-Yau categories and noncommutative projective geometry.
Research group chair
Professor Milen Yakimov is renowned for his contributions to noncommutative algebra, representation theory, and cluster algebras. He received his undergraduate degree in Mathematics from Sofia University, Bulgaria, in 1996, and completed his PhD at the University of California, Berkeley, in 2001. His research explores the deep connections between noncommutative algebra, triangulated categories, Poisson geometry, and integrable systems, placing him at the forefront of modern algebraic research.
Throughout his career, Professor Yakimov has been recognized with several prestigious honors, including a Sloan Research Fellowship in 2005 and election as a Fellow of the American Mathematical Society in 2018. His research has been continuously supported by the National Science Foundation since 2004, reflecting the sustained impact of his work in the mathematical sciences. At Northeastern, he is an integral member of the algebra group, contributing to a vibrant research community that engages with areas such as algebraic geometry, quantum groups, and their applications to combinatorics, topology, and physics.
Team
Emine Yıldırım, R3 - Established Researcher
Emine Yıldırım obtained her PhD from Université du Québec à Montréal in 2018 under the supervision of Professor Hugh She was awarded the highly selective Simons Postdoctoral Fellowship at the Isaac Newton Institute & University of Cambridge, UK between October 2021 and September 2022. Before coming to ICMS, between October 2022 and July 2025, she was a Research Fellow at the University of Leeds, UK. Yildirim’s research interests are in the field of representation theory of algebras, cluster algebras and related combinatorics which includes surface triangulations, friezes, lattices, dynamical actions.
Deepanshu Prasad, R2 - Recognised Researcher
Deepanshu Prasad received his Ph.D in Mathematics from Queen’s University, Canada in 2025 under Charles Paquette and David Wehlau. His research explores the connection between representation theory, algebraic geometry, and cluster algebras, with contributions to the structure of semi-invariant rings, quiver representations, and mutations. He co-authored preprints extending the Sato-Kimura theorem and establishing new results on Galois coverings and τ-rigidity. His trajectory is marked by multiple competitive awards including the Norman and Grace Miller Fellowship and Queen’s University Research Fellowship.
Wonwoo Kang, R2 - Recognised Researcher
Wonwoo Kang earned his Ph.D. in Mathematics at the University of Illinois at Urbana-Champaign (UIUC) under the supervision of Professor Rinat Kedem. His research focuses on cluster algebras and their connections to combinatorics and algebraic geometry. Kang’s recent work involves developing combinatorial formulas and skein relations for elements in cluster algebras arising from punctured surfaces. Another line of his recent research investigates unimodal structures in F-polynomials associated with surface-type cluster algebras, revealing new combinatorial links with poset theory.
Nicola Bellumat, R2 - Recognised Researcher
Nicola Bellumat received his PhD from the University of Sheffield, UK in 2021. During his postgraduate studies his research focus was in algebraic topology: more precisely, chromatic homotopy theory and Bousfield localization. Bellumat carried out his first postdoctoral position at the Aarhus University, Denmark and his interests moved towards tensor triangulated categories and their theory of stratification via Balmer-Favi support recently developed by Barthel, Heard and Sanders. Currently, he is working on the relation between the local-to-global principle and the topology of the Balmer spectrum.
Activities and Announcements
Contacts
Prof. Milen Yakimov
International Center for Mathematical Sciences – Sofia
Institute of Mathematics and Informatics, BAS
Bulgaria, Sofia, 1113, Acad. George Bonchev str. bl 8
milenyakimov@gmail.com
