INTEGRABLE SYSTEMS AND GEOMETRY OF MODULI SPACES

Center of Integrable Systems (CIS) at the Yaroslavl State University (YarSU) and

Laboratory of Algebraic Geometry (LAG) at the National Research University Higher School of Economics, Moscow (NRU HSE)

will organize the INTERNATIONAL CONGRESS of MATHEMATICIANS 2022 SATELLITE CONFERENCE ”INTEGRABLE SYSTEMS AND GEOMETRY OF MODULI SPACES”

The conference will take place in Yaroslavl at 18-22 July 2022

 

Mathematical physics and in particular the theory of integrable systems have always been the area of important applications and a source of new useful concepts in algebraic geometry. In the 19th century problems of separation of variables in the geodesic problem on ellipsoid led to the Jacobi inversion problem for Abel maps, Jacobi varieties and motivated further development of the theory of abelian functions. The creation of the soliton theory in 1960s reinvigorated the link between two disciplines, which still continues to flourish and includes the modern theory of moduli spaces. The Hitchin integrable systems on the moduli spaces of stable vector bundles, Calogero-Moser spaces, Gromov-Witten invariants, topological recursion, Frobenius manifolds, cohomological field theory and their relations with integrable hierarchies are just a few manifestations of the important modern developments at the crossroad between algebraic geometry and integrable systems.

The conference aims at assessing the state of the art on various aspects of integrable systems, the geometry of moduli spaces and defining directions for future developments. We aim at gathering people with complementary expertise from the both sides of the interface. This could lead to new fruitful collaborations and further development of algebraic geometry and the theory of integrable systems.

The topics covered by the conference will include, but not restricted to: 

  • 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, Teichm\"uller 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 belong to the area of the very active research both in pure mathematics and mathematical physics, which includes in particular representation theory, enumerative geometry, random matrix theory and quantum field theory. We believe that for this reason this conference will attract considerable interest from both mathematics and theoretical physics communities. Many top experts in these areas from different countries of Europe, America, Asia and Australia have already agreed to attend and give talks at the conference.