Goncharov won a gold medal at the International Mathematical Olympiad in 1976. He attained his doctorate at Lomonosov Moscow State University in 1987, under supervision of Israel Gelfand with thesis Generalized conformal structures on manifolds. Goncharov was an Invited Speaker at the 1994 International Congress of Mathematicians and gave a talk Polylogarithms in arithmetic and geometry.
- Geometry of configurations, polylogarithms, and motivic cohomology. Adv. Math. 114 (1995), no. 2, 197–318.
- (with A. M. Levin) Zagier's conjecture on L(E,2). Invent. Math. 132 (1998), no. 2, 393–432.
- Volumes of hyperbolic manifolds and mixed Tate motives. J. Amer. Math. Soc. 12 (1999), no. 2, 569–618.
- (with P. Deligne) Groupes fondamentaux motiviques de Tate mixte. Ann. Sci. École Norm. Sup. (4) 38 (2005), no. 1, 1–56.
- (with V. V. Fock) Moduli spaces of local systems and higher Teichmüller theory. Publ. Math. Inst. Hautes Études Sci. No. 103 (2006), 1–211.
- (with V. V. Fock) The quantum dilogarithm and representations of quantum cluster varieties. Invent. Math. 175 (2009), no. 2, 223–286.
- (with H. Gangl, A. Levin) Multiple logarithms, algebraic cycles and trees, in Pierre Cartier et al. Frontiers in Number Theory, Physics and Geometry, vol. 2, Springer Verlag 2007
- (with V. V. Fock) Cluster ensembles, quantization and the dilogarithm. Ann. Sci. Éc. Norm. Supér. (4) 42 (2009), no. 6, 865–930.
- (with R. Kenyon) Dimers and cluster integrable systems. Ann. Sci. Éc. Norm. Supér. (4) 46 (2013), no. 5, 747–813
- (with T. Dimofte, M. Gabella) K-Decompositions and 3d Gauge Theories. ArXiv
- (with J. Golden, M. Spradlin, C. Vergu, A. Volovich) Motivic Amplitudes and Cluster Coordinates. ArXiv