Mathematical physics and, in particular, the theory of integrable systems have always been areas of important application and sources of useful new concepts in algebraic geometry. In the 19th century, issues with separating variables in the geodesic problem on an ellipsoid led to the Jacobi inversion problem for Abel maps, Jacobi varieties, and further development of the theory of abelian functions. The introduction of the soliton theory in the 1960s reinvigorated the link between the two disciplines, which flourishes to this day and includes the modern theory of moduli spaces. The Hitchin integrable system on the moduli spaces of stable vector bundles, Calogero-Moser spaces, Gromov-Witten invariants, topological recursion, Frobenius manifolds, cohomological field theory, and their relation to integrable hierarchies are just a few manifestations of important modern developments at the intersection of algebraic geometry and integrable systems.
The topics covered by the conference will include:
- Cohomological field theories and deformations of integrable hierarchies,
- Enumerative geometry, moduli spaces, and integrable hierarchies,
- Multi-Hamiltonian integrability in commutative and non-commutative settings,
- Poisson geometry, Teichmüller theory, and cluster algebras,
- Quantum integrable systems, quantum groups, and Cherednik algebras,
- Hitchin type integrable systems and geometric Langlands correspondence,
- Gaudin models, Bethe algebras, and degenerations,
- Nakajima quiver varieties and representation theory,
- Moduli spaces of stable sheaves on algebraic varieties,
- Moduli spaces in derived category (Bridgeland stability, tilt-stability),
- Donaldson-Thomas theory,
- Higgs sheaves, decorated sheaves,
- Connections, local systems, constructable sheaves.
These topics are the subjects of active research both in pure mathematics and mathematical physics, which particularly includes representation theory, enumerative geometry, random matrix theory, and quantum field theory. We believe that for this reason the conference will attract considerable interest from the mathematics and theoretical physics communities alike. Many top experts in these areas from countries in Europe, the Americas, and Asia have already agreed to attend and give talks at the conference.