Spectral Networks

Preface.-Motivation and Historical Perspective.-I. Mathematical Foundation.- 1.The Fundamental Group.-2.Covering Spaces.-3.Bundles and Connections.-4.Hyperbolic Geometry.- 5.Cluster Varieties.- II Higher-rank Teichmueller Theory.-6. The Teichmueller Space.-7.Coordinates on Teichmueller Space.-8.differentials on a Riemann Surface.-9.Higher-rank Teichmueller Spaces.- 10.Hitchin Representations.-11.Maximal Representations.-12.Positivity.- III Spectral Networks in Geometry.-13.Non-degenerate Spectral Networks.-14.Combinatorial and Analytic Construction.-15.Non-abelianization and Abelianization.-16.WKB Method and Stokes Graphs.- IV Counting BPS States.-17.Four-dimensional Supersymmetric Quantum Field Theories.-18.Four-dimensional N=2 Gauge Theories.-19.Electric-magnetic Duality.-20.Seiberg-Witten Theory.-21.Theories of Class S.-22.BPS States in Class S Theories.- V Generalizations.-23.Exponential Networks.-24.Three-dimensional Networks.-25.WKB Cameral Networks.-26.Nonabelianization for Conformal Virasoro Blocks.

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• Geometria diferencial e riemaniana
• Análise complexa, variáveis ??complexas
• A física quântica (mecânica quântica e teoria quântica de campos)
• Teoria matemática da computação

Open Access;Spectral networks;Character varieties and moduli spaces of flat connections;Higher-rank Teichmueller theory;Cluster varieties;Supersymmetric gauge theories;Seiberg-Witten theory;Class S theories;Fock-Goncharov theory;Moduli spaces of flat connections;Electric-magnetic duality