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Regular version of the site

International Laboratory of Representation Theory and Mathematical Physics

Geometric Methods in Physics XXXVI

Orlov A. Y.

Springer, 2019.

Strict versions of integrable hierarchies in pseudodifference operators and related Cauchy problems

Хельминк Г. Ф., Poberezhny V. A., Поленкова С. В.

Theoretical and Mathematical Physics. 2019. Vol. 198. No. 2. P. 197-214.

Book chapter
From Reflection Equation Algebra to Braided Yangians

Saponov P. A., Gurevich D.

In bk.: Recent Developments in Integrable Systemsand Related Topics of Mathematical Physics. Vol. 273. Springer, 2018. P. 107-129.

Working paper
New series of moduli components of rank 2 semistable sheaves on P3 with singularities of mixed dimension

Aleksei Ivanov-Viazemsky.

arXiv:1903.00772. math.AG. Cornell University, 2019

The main objective of the laboratory is to develop a common approach to a variety of issues at the interface between the theory of integrable systems and representation theory of quantum and infinite-dimensional groups and algebras.

Research are conducted in several inter-related directions and involves close cooperation between mathematicians and mathematical physicists.

These areas include:

  1. Quantum cohomology in the theory of integrable systems;
  2. Questions of mirror symmetry;
  3. Multidimensional hypergeometric functions and geometric representation theory;
  4. Elliptic conformal blocks and elliptic hypergeometric functions;
  5. Geometric Langlands correspondence;
  6. Combinatorial development, homology and geometric methods in the theory of moduli spaces of various geometric and analytic structures with applications to problems of mathematical physics.