Reddening Sequences for Cluster Algebras

Explore the concept of reddening sequences in cluster algebras through this 44-minute lecture by Volker Genz from the Institut des Hautes Etudes Scientifiques (IHES). Delve into the significance of reddening sequences as a relaxed notion of finiteness in cluster algebras, which are generally not finitely generated. Examine the far-reaching consequences of reddening sequences, including generic finite dimensionality of the Jacobian, numeric Donaldson-Thomas invariants, and canonical bases. Investigate specific cases where reddening sequences have been established, despite the challenges in determining their existence for all cluster algebras. Follow the lecture's structure, covering topics such as introduction to cluster algebras, examples, consequences, parametrization, invariance, and key ingredients. Gain insights into general estimation rules and utilize the Sage window for practical applications. Conclude with a comprehensive understanding of reddening sequences and their importance in the study of cluster algebras.