On cluster algebras and topological string theory

Semenyakin, M. (2022)

Doctoral Thesis

My PhD research is devoted to studies of the conjectural cluster-algebraic symmetry in the theory of topological string, which is the simplest, however already non-trivial sector in the theory of string. The language of cluster algebras is the modern tool which was initially developed for solving problems in linear algebra, and has recently been applied to the theory of integrable systems. In this dissertation we identify the cluster-algebraic nature of new classes of integrable systems of string-theoretic origin. We then show how the partition functions of topological string on the corresponding geometries can be naturally fit into a cluster-algebraic context.

• Topological string
• Cluster algebras
• Integrable systems
• Seiberg-Witten theory

• All authors: Semenyakin, M.
• Supervisor: Beenakker, C.W.J.; Marshakov, A.V.
• Committee: Grassi, A.; Nekrasov, N.; Shapiro, M.; Aarts, J.; Schalm, K.E.; Cheianov, V.
• Qualification: Doctor (dr.)
• Awarding Institution: Leiden Institute of Physics (LION), Faculty of Science, Leiden University
• Date: 2022-09-15
• Title of host publication: Casimir PhD Series
• ISBN (print): 9789085935346
• Name: 2022-24