nLab Alexander Goncharov

Alexander B. Goncharov

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Selected writings

Introducing Fock-Goncharov coordinates on moduli spaces of flat connections:

• Vladimir V. Fock, Alexander B. Goncharov, Moduli spaces of local systems and higher Teichmüller theory, Publ. Math. Inst. Hautes Études Sci. 103, 1-211 (2006) [arXiv:math/0311149, doi:10.1007/s10240-006-0039-4]

On Poisson-Lie groups in viewpoint of cluster varieties:

• Vladimir V. Fock, Alexander B. Goncharov, Cluster X-varieties, amalgamation and Poisson-Lie groups, in: Algebraic Geometry and Number Theory, Progress in Mathematics 253, Birkhäuser (2006) 27-68 [arxiv:math/0508408, doi:10.1007/978-0-8176-4532-8_2]

About quantum dilogarithm

• A.B. Goncharov, The pentagon relation for the quantum dilogarithm and quantized $M_{0,5}$, arxiv:0706.4054

• V. V. Fock, A. B. Goncharov, The quantum dilogarithm and representations of quantum cluster varieties, arXiv:math.QA/0702397

• V. V. Fock, A. B. Goncharov, Cluster ensembles, quantization and the dilogarithm II: The intertwiner, arXiv:math.QA/0702398

On Hodge theory, periods, motives and motivic expressions in QFT

• A. B. Goncharov, Periods and mixed motives, math.AG/0202154
• Alexander Goncharov, Regulators, In: Algebraic K-theory Handbook (arXiv:0407308)
• A. B. Goncharov, Polylogarithms and Motivic galois groups, (pdf)
• A. B. Goncharov, Hodge correlators, arXiv:0803.0297, Hodge correlators II, arXiv:0807.4855

Monograph

• Nima Arkani-Hamed, Jacob Bourjaily, Freddy Cachazo, Alexander Goncharov, Alexander Postnikov, Jaroslav Trnka, Grassmannian geometry of scattering amplitudes, Cambridge Univ. Press 2016

category: people