Доклады    в   2014   году

• November 13
  Andrei Bytsko (POMI)
  "On representations of Temperley-Lieb algebra"
  

• July 31
  Fedor Smirnov
  "Одноточечные функции в модели sinh-Гордон и коэффициент отражения для модели Лиувилля"
  

• July 24
  Andrei Bytsko, PDMI
  "Tetrahedron equation, Weyl group, and quantum dilogarithm"
  

  The tetrahedron equation is a 3-simplex analogue of the Yang-Baxter equation. It will be shown how solutions to the quantum tetrahedron equation involving quantum dilogarithms are related to a multi-parameter quantum group and the longest element of the Weyl group. The talk is based on a joint work with A. Volkov.

• July 17
  Pasha Mnev, PDMI
  "Cellular abelian BF theory with Segal-like gluing property"
  

  We give a combinatorial construction of quantum abelian BF theory on cobordisms endowed with cellular subdivisions, with subdivision-invariant partition functions featuring Atiyah-Segal-type gluing property with respect to sewing of cobordisms, and retaining an appropriate gauge-invariance property. Partition functions are generally expressed in terms of R-torsion and the propagator connecting the in- and out-boundaries, and contain (in case of a non-acyclic local system) a peculiar complex phase, a power of e^{i\pi/8}. Along the way, we obtain a nontrivial gluing formula for propagators (Green's functions for cellular coboundary operator) via techniques of homological perturbation theory; this formula works with minor modifications also in "continuum" (as opposed to cellular) field theory with kinetic term given by de Rham operator. This is a part of the ongoing joint work with A.S.Cattaneo and N.Reshetikhin.

• May 22
  Vitaly Tarasov, PDMI
  "Lower estimates for numbers of real solutions in Schubert calculus problems via Gaudin model"
  

• 6 февраля
  Л. Д. Фаддеев
  "Спектральная теория для оператора u+u^{-1}+v, где u и v - пара Вейля uv=q^2vu"
  

• 30 января
  С. Деркачев
  "Собственные функции матричных элементов матрицы монодромии (A,B,C,D)"
  

  Задача о диагонализации операторов A(u),B(u),C(u),D(u) -- элементов матрицы монодромии, возникает в различных контекстах. Например, в методе разделения переменных Склянина важную роль играют собственные функции оператора B(u). Мы рассмотрим итерационную процедуру построения собственных функций и вычисления их скалярных произведений на примере оператора D(u) в модели sl(2,R)-инвариантной XXX_s спиновой цепочки.

• 23 января
  Pavel Mnev
  "Classical free boson on Lorentzian surfaces with boundary"
  

  For a large class of classical field theories on manifolds with boundary, solutions of the Euler-Lagrange equations induce a Lagrangian submanifold in the phase space associated to the boundary. E.g. this is so for theories admitting a Hamiltonian formulation, considered on cylinders. We will consider a system which does not admit a reasonable Hamiltonian description - 2D free massless boson on a compact domain on Minkowski plane, and will sketch the proof that Lagrangianity of the evolution relation still holds (which provides grounds for the geometric quantization of this system). On more general Lorentzian surfaces however the evolution relation may fail to be Lagrangian, e.g. for the Misner cylinder.

• 16 января
  N. Yu. Reshetikhin
  "Quantum 6j symbols"