Algebraic and symplectic geometry, moduli spaces of coherent sheaves, homological and homotopical algebra, geometric quantization, mathematical physics, Diophantine approximations.
Main publications:
A. L. Gorodentsev, “Perestroiki isklyuchitelnykh rassloenii na $\mathbf P^n$”, Izv. AN SSSR. Ser. matem., 52:1 (1988), 3–15; Math. USSR-Izv., 32:1 (1989), 1–13
A. L. Gorodentsev, “Isklyuchitelnye rassloeniya na poverkhnostyakh s podvizhnym antikanonicheskim klassom”, Izv. AN SSSR. Ser. matem., 52:4 (1988), 740–757; Math. USSR-Izv., 33:1 (1989), 67–83
A. L. Gorodentsev, “Exceptional objects and mutations in derived categories”, Helices and vector bundles, London Math. Soc. Lecture Note Ser., 148, Cambridge Univ. Press, Cambridge, 1990, 57–73
A. L. Gorodentsev, “Helix theory and nonsymmetrical bilinear forms”, Algebraic geometry and its applications, Proceedings of the 8th algebraic geometry conference (Yaroslavl' 1992), Aspects of Math., E25, Vieweg, Braunschweig, 1994, 47–59
A. L. Gorodentsev, A. N. Tyurin, “Abeleva lagranzheva algebraicheskaya geometriya”, Izv. RAN. Ser. matem., 65:3 (2001), 15–50; Izv. Math., 65:3 (2001), 437–467
A. L. Gorodentsev, S. A. Kuleshov, “Helix theory”, Mosc. Math. J., 4:2 (2004), 377–440
A. L. Gorodentsev, S. A. Kuleshov, A. N. Rudakov, “t-stabilnosti i t-struktury na triangulirovannykh kategoriyakh”, Izv. RAN. Ser. matem., 68:4 (2004), 117–150; Izv. Math., 68:4 (2004), 749–781
A. L. Gorodentsev, A. S. Khoroshkin, A. N. Rudakov, “On syzygies of highest weight orbits”, Moscow Seminar on Mathematical Physics, II, Amer. Math. Soc. Transl. Ser. 2, 221, Amer. Math. Soc., Providence, RI, 2007, 79–120
; Math. USSR-Izv., 32:1 (1989), 
