Доклады    в   2009   году

• 24 December
  P.P.Kulish
  "Jordanian deformation of XXX-spin chain with non-periodic boundary condition"
  

  Non-periodic boundary conditions consistent with integrability properties of a modle are defined by reflection K-matricies - solutions of the reflection equations. These K-matricies are constructed for jordanian deformation of the SL(2) invariant R-matrix. Spectra of corresponding deformed XXX-model are discussed.

• October 29
  I.E.Shenderovich
  "Beyond 1/N expansion: statistical mechanics of multi-trace operators"
  

  We discuss the renormalization of multi-trace operators in N=4 SYM theory. We show that some interesting effects like phase transitions arise beyond 1/N expansion. This phase transition may be dual to the Hawking-Page phase transition in AdS black hole. Some questions about quantum corrections to this effect are still open.

• October 22
  P.N.Mnev
  "One-dimensional simplicial Chern-Simons theory"
  

• July 30
  A.Yu.Volkov
  "On hypothesis of Alexei Zamolodchikov"
  

• May 28
  V. Tarasov
  "On the Gaudin model and Cherednik algebras"
  

  I discuss the Gaudin model on a tensor product of the vector representations of the Lie algebra gl_N and the algebra of commuting integrals of motion acting on the "zero" weight subspace. This algebra turns out to be isomorphic to the center of the rational Cherednik algebra of type A. The isomorphism involves a nice factorization construction.

• 2 апреля
  П.П. Кулиш
  "Симметрия квантовой группы интегрируемых спиновых систем
  (Бирман - Вензл - Мураками алгебра)"
  

  Integrable open spin chains related to the quantum affine algebras U_q(o(3)) and U_q(A_2^(2)) are considered. Hamiltonian (and other integrals) belongs to the Birman-Wenzl-Murakami algebra (BMW). The symmetry algebra U_(o(3)) and the BMW-algebra centralize each other in the spin chain representation space. Consequently the multiplet structure of the energy spectra is obtained.

• 5 марта
  S.Derkachov
  "Renormalization of composite operators in (super) Yang-Mills theory, MHV-amplitudes and integrability"
  

  We are going to duscuss two topics:
  1) the problem of renormalization of composite operators in Yang-Mills theory and its connection XXX-spin chain model.
  2) calculation of the MHV-amplitudes in Yang-Mills theory.

• 26 февраля
  A.N. Kirillov (RIMS, Japan)
  "Saga on Dunkle operators" "