Integrable systems have deep connections with many areas of mathematics and theoretical physics, including quantum field theory, statistical mechanics, representation theory, geometry, and topology. In recent years, the field has broadened considerably, with new directions emerging at the interfaces between different areas of mathematics and theoretical physics.

Unbeaten Tracks in Integrability brings together researchers working along these different directions, with particular emphasis on connections between research traditions that have so far remained relatively unexplored. The workshop aims to create a setting in which new problems, structures, and methods can emerge from interaction across these boundaries.

Topics include:

• Quantum groups, the Yang–Baxter equation, and quantum integrable systems
• The tetrahedron equation, higher-dimensional integrable models, and higher algebraic structures
• Integrable field theories and sigma models, including integrable deformations
• Four-dimensional Chern–Simons theory and its higher-dimensional generalizations
• Integrable boundaries, defects, and interfaces
• Integrability in string theory, gauge/gravity duality, and supersymmetric field theory
• Quantum curves, dimer models, and related geometric methods
• Integrable structures in conformal field theory, vertex algebras, algebraic geometry, and related areas