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Workshop Aug 2010

Quantum Dilogarithm and Quantum Teichmueller Theory

2012.10.17 | Christine Dilling

Date Mon 09 Aug Fri 13 Aug
Time 09:00    16:00
Location QGM, Aarhus University


A classical dilogarithm L(x) is very well known function,which has many applications in number theory,algebraic K-theory,geometry and topology of hyperbolic three-manifolds,representations of Virasoro and Kac-Moody algebras,conformal field theory,...(see [2} ). A quantum dilogarithm L(x,q) (see [1]) is an interesting "non-commutative" generalization of L(x). In principle there are several different versions of a classical dilogarithm as well as quantum one (see [4] for another modern application and also for interesting historical study). Surprisingly one of quantum versions of dilogarithm goes back to 19 century.

List of references:
[1] L.D.Faddeev,R.M.Kashaev,Quantum Dilogarithm,arXiv,hep-th,1993
[2] V.V.Bazhanov and N.Yu. Reshetikhin, Remarks on the quantum dilogarithm, J.Phys.A:Math.Gen.28 1995),2217-2226.
[3] R.M.Kashaev,The hyperbolic volume of knots from the quantum dilogarithm, Letters in mathematical physics,vol 39,n3,1997.
[4] V.V.Fock,A.B.Goncharov,The quantum dilogarithm and representations of quantum cluster varieties, arXiv(math.QA),2008

Poster PDFProgramme

09.00-10.00 Registration by Aud. D2
10.00-11.00 Opening lecture of Ludwig Faddeev (Steklov Institute)
"Quantum dilogarithm, its advent and some applications"11.00-11.30 Coffee break
11.30-12.30 Rinat Kashaev (University of Geneva)
"Tetrahedral symmetries of the quantum dilogarithm"
12-30-14.00 Lunch
14.00-15.00 Tomoki Nakanishi (Nagoya University)
"Dilogarithm identities in conformal field theory and cluster algebras"
15.15-16.15 Jörg Teschner (Universität Hamburg)
"Quantization of Teichmueller spaces vs. quantization of Hitchin moduli spaces"

10.00-11.00 Vladimir Fock (University of Strasbourg)
"Geometric quantization of cluster varieties and quantum dilogarithm"
1.00-11.30 Coffee break
11.30-12.30 Alexander Volkov (Steklov Mathematical Institute)
"On the Periodicity Conjecture for Y-systems"
12.30-14.00 Lunch
14.00-15.00 Petr Kulish (Steklov Institute)
"Quantum integrable systems and generalized Schur-Weyl duality"
15.15-16.00 Informal discussions

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