Infinite Analysis Seminar Tokyo
Seminar information archive ~12/07|Next seminar|Future seminars 12/08~
Date, time & place | Saturday 13:30 - 16:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
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2007/11/17
13:00-16:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Gleb Novichkov (Keio Univ.) 13:00-14:30
Dynamical r-matrices coupled with dual Poisson Lie group
Yang-Baxter Equation and Quantum Geometry
Gleb Novichkov (Keio Univ.) 13:00-14:30
Dynamical r-matrices coupled with dual Poisson Lie group
[ Abstract ]
The notion dynamical r-matrix coupled with Poisson manifold
is a natural generalization of the notion of the classical
dynamical r-matrix. We will consider special case when
Poisson manifold is a dual Poisson Lie group. We discuss
necessary conditions for the existence dynamical r-matrices
coupled with dual Poisson Lie groups and provide
some examples. We will also discuss some open questions
and possible relations to other subjects.
Vladimir V. Bazhanov (Australian National Univ.) 15:00-16:30The notion dynamical r-matrix coupled with Poisson manifold
is a natural generalization of the notion of the classical
dynamical r-matrix. We will consider special case when
Poisson manifold is a dual Poisson Lie group. We discuss
necessary conditions for the existence dynamical r-matrices
coupled with dual Poisson Lie groups and provide
some examples. We will also discuss some open questions
and possible relations to other subjects.
Yang-Baxter Equation and Quantum Geometry
[ Abstract ]
We demonstrate that certain integrable models
of statistical mechanics and quantum field theory
can be interpreted as quantization's of objects
of classical discrete geometry.
The fluctuating variables in these models take continuous
values. The classical geometry corresponds to stationary
configurations in the quasi-classical (or zero-temperature)
limit of the quantum system.
Our main example is the Faddeev-Volkov model which describes
the quantization of the circle patterns and associated with
the Thurston's discrete analogue of the Riemann mapping theorem
(discrete conformal transformations of the 2D plane).
Other examples will be also considered.
Finally we will discuss the geometric origins of integrability
which stem from from the classical results of Lam\\'e,
Darboux and Bianchi in differential geometry.
We demonstrate that certain integrable models
of statistical mechanics and quantum field theory
can be interpreted as quantization's of objects
of classical discrete geometry.
The fluctuating variables in these models take continuous
values. The classical geometry corresponds to stationary
configurations in the quasi-classical (or zero-temperature)
limit of the quantum system.
Our main example is the Faddeev-Volkov model which describes
the quantization of the circle patterns and associated with
the Thurston's discrete analogue of the Riemann mapping theorem
(discrete conformal transformations of the 2D plane).
Other examples will be also considered.
Finally we will discuss the geometric origins of integrability
which stem from from the classical results of Lam\\'e,
Darboux and Bianchi in differential geometry.