Cluster Algebras, Hall Algebras and Their Applications
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Organizer(s): |
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Affiliation:
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Country:
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Xueqing Chen
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University of Wisconsin-Whitewater
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USA
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Fang Li
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Zhejiang University
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Peoples Rep of China
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Min Huang
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Sun Yat-sen University (Zhuhai Campus)
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Peoples Rep of China
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Introduction:
| | Cluster algebras and Hall algebras lie at the interface of representation theory, topology, algebraic geometry and combinatorics. Since their introduction by Fomin and Zelevinsky in 2001, cluster algebras have profoundly influenced numerous areas including quiver representations, Teichmüller theory, Poisson geometry, dynamical system and mathematical physics. Hall algebras, originally conceived to study the category of finite-dimensional modules over finite fields, have found deep connections with quantum groups, Donaldson–Thomas invariants, and categorification.
The proposed session aims to bring together leading experts, early-career researchers, and graduate students to explore current trends, open problems, and emerging applications of cluster algebras and Hall algebras. Potential topics for discussion encompass advancements in cluster algebras, quantum cluster algebras, cluster categories, monoidal categories, stability conditions, scattering diagrams, derived Hall algebra, cohomological Hall algebras, quiver Hecke algebras, and the interplay between cluster theory and Lie theory. We expect that this conference will promote the progress of some key issues in the frontier of mathematics.
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