Algebraic geometry and noncommutative algebraic geometry, homological algebra, categories of (quasi)coherent sheaves, derived and triangulated categories, mirror symmetry.
Main publications:
Orlov D.O., “Equivalences of derived categories and K3 surfaces”, J. Math. Sci. (New York), 84:5 (1997), 1361–1381
Bondal, Alexei; Orlov, Dmitri, “Reconstruction of a variety from the derived category and groups of autoequivalences”, Compositio Mathematica, 125:3 (2001), 327–344
Orlov D.O., “Triangulated categories of singularities and D-branes in Landau–Ginzburg models”, Algebr. Geom. Metody, Svyazi i Prilozh., Tr. Mat. Inst. Steklova, 246, 2004, 240–262 (Russian) ; Engl. transl. Proc. Steklov Inst. Math., 246:3 (2004), 227–248
Orlov, Dmitri, “Derived categories of coherent sheaves and triangulated categories of singularities”, Algebra, arithmetic, and geometry: in honor of Yu. I. Manin, v. II, Progr. Math., 270, Birkhäuser, Boston, MA, 2009, 503–531
Lunts, Valery A.; Orlov, Dmitri O., “Uniqueness of enhancement for triangulated categories”, J. Amer. Math. Soc., 23:3 (2010), 853–908
V. Alexeev, D. Orlov, “Derived categories of Burniat surfaces and exceptional collections”, Math. Ann., 2013 (to appear) , arXiv: 1208.4348
2.
M. Abouzaid, D. Auroux, A. I. Efimov, L. Katzarkov, D. Orlov, “Homological mirror symmetry for punctured spheres”, J. Amer. Math. Soc., 2013 (to appear) , arXiv: 1103.4322
3.
A. Canonaco, D. Orlov, P. Stellari, “Does full imply faithful?”, J. Noncommut. Geom., 7:2 (2013), 357–371, arXiv: 1101.5931
4.
S. Gorchinskiy, D. Orlov, “Geometric Phantom Categories”, Publ. Math. Inst. Hautes. Études. Sci., 117:1 (2013), 329–349, arXiv: 1209.6183
5.
D. Orlov, “Matrix factorizations for nonaffine LG–models”, Math. Ann., 353:1 (2012), 95-108, arXiv: 1101.4051
6.
D. Orlov, “Formal completions and idempotent completions of triangulated categories of singularities”, Adv. Math., 226:1 (2011), 206–217, arXiv: 0901.1859
7.
A. I. Efimov, V. A. Lunts, D. O. Orlov, “Deformation theory of objects in homotopy and derived categories III: Abelian categories.”, Adv. Math., 226:5 (2011), 3857–3911, arXiv: math/0702840
8.
D. Orlov, Landau-Ginzburg Models, D-branes, and Mirror Symmetry, 2011, 25 pp., arXiv: 1111.2962
9.
A. I. Efimov, V. A. Lunts, D. O. Orlov, “Deformation theory of objects in homotopy and derived categories. II. Pro-representability of the deformation functor”, Adv. Math., 224:1 (2010), 45–102., arXiv: math/0702839
10.
V. A. Lunts, D. O. Orlov, “Uniqueness of enhancement for triangulated categories”, J. Amer. Math. Soc., 23:3 (2010), 853–908, arXiv: 0908.4187
11.
A. I. Efimov, V. A. Lunts, D. O. Orlov, “Deformation theory of objects in homotopy and derived categories. I. General theory”, Adv. Math., 222:2 (2009), 359–401, arXiv: math/0702838
12.
Dmitri Orlov, “Remarks on generators and dimensions of triangulated categories”, Mosc. Math. J., 9:1 (2009), 143–149, arXiv: 0804.1163
13.
A. Kapustin, L. Katzarkov, D. Orlov, M. Yotov, “Homological Mirror Symmetry for manifolds of general type”, Cent. Eur. J. Math., 7:4 (2009), 571–605, arXiv: 1004.0129
14.
D. Orlov, “Derived categories of coherent sheaves and triangulated categories of singularities”, Algebra, arithmetic, and geometry, In honor of Yu. I. Manin on the occasion of his 70th birthday, v. II, Progr. Math., 270, Birkhäuser Boston, Inc., Boston, MA, 2009, 503–531
15.
D. Auroux, L. Katzarkov, D. Orlov, “Mirror symmetry for weighted projective planes and their noncommutative deformations”, Ann. of Math. (2), 167:3 (2008), 867–943
16.
D. Orlov, A. Vishik, V. Voevodsky, “An exact sequence for $K^{M}_{*}/2$ with applications to quadratic forms”, Ann. of Math. (2), 165:1 (2007), 1–13
17.
D. Auroux, L. Katzarkov, D. Orlov, “Mirror symmetry for del Pezzo surfaces: vanishing cycles and coherent sheaves”, Invent. Math., 166:3 (2006), 537–582
18.
D. O. Orlov, “Triangulated categories of singularities and equivalences between Landau–Ginzburg models”, Sb. Math., 197:12 (2006), 1827–1840
19.
D. O. Orlov, “Derived categories of coherent sheaves and motives”, Russian Math. Surveys, 60:6 (2005), 1242–1244
20.
A. N. Kapustin, D. O. Orlov, “Lectures on mirror symmetry, derived categories, and D-branes”, Russian Math. Surveys, 59:5 (2004), 907–940
21.
D. O. Orlov, “Triangulated Categories of Singularities and D-Branes in Landau–Ginzburg Models”, Proc. Steklov Inst. Math., 246 (2004), 227–248
22.
A. Kapustin, D. Orlov, “Remarks on A-branes, mirror symmetry, and the Fukaya category”, J. Geom. Phys., 48:1 (2003), 84–99
23.
A. Kapustin, D. Orlov, “Vertex algebras, mirror symmetry, and D-branes: the case of complex tori”, Comm. Math. Phys., 233:1 (2003), 79–136
24.
D. O. Orlov, “Quasi-coherent sheaves in commutative and non-commutative geometry”, Izv. Math., 67:3 (2003), 535–554
25.
D. O. Orlov, “Derived categories of coherent sheaves and equivalences between them”, Russian Math. Surveys, 58:3 (2003), 511–591
26.
A. Bondal, D. Orlov, “Derived categories of coherent sheaves”, Proceedings of the International Congress of Mathematicians (Beijing, 2002), Vol. II, Higher Ed. Press, Beijing, 2002, 47–56
27.
D. O. Orlov, “Derived categories of coherent sheaves on Abelian varieties and equivalences between them”, Izv. Math., 66:3 (2002), 569–594
28.
A. Kapustin, A. Kuznetsov, D. Orlov, “Noncommutative instantons and twistor transform”, Comm. Math. Phys., 221:2 (2001), 385–432
29.
V. Golyshev, V. Lunts, D. Orlov, “Mirror symmetry for abelian varieties”, J. Algebraic Geom., 10:3 (2001), 433–496
30.
A. Bondal, D. Orlov, “Reconstruction of a variety from the derived category and groups of autoequivalences”, Compositio Math., 125:3 (2001), 327–344
31.
D. O. Orlov, “Equivalences of derived categories and $K3$ surfaces”, Algebraic geometry, 7, J. Math. Sci. (New York), 84:5 (1997), 1361–1381
S. A. Kuleshov, D. O. Orlov, “Exceptional sheaves on del Pezzo surfaces”, Izv. RAN. Ser. matem., 58:3 (1994), 53–87; S. A. Kuleshov, D. O. Orlov, “Exceptional sheaves on del Pezzo surfaces”, Russian Acad. Sci. Izv. Math., 44:3 (1995), 479–513
34.
D. O. Orlov, “Projective bundles, monoidal transformations, and derived categories of coherent sheaves”, Izv. RAN. Ser. matem., 56:4 (1992), 852–862; D. O. Orlov, “Projective bundles, monoidal transformations, and derived categories of coherent sheaves”, Russian Acad. Sci. Izv. Math., 41:1 (1993), 133–141
35.
D. O. Orlov, “Exceptional set of vector bundles on the variety $V_5$”, Moscow Univ. Math. Bull., 46:5 (1991), 48–50
36.
L. V. Katsarkov, D. O. Orlov, “Prym varieties of hyperelliptic curves and their applications to nonlinear equations”, Moscow Univ. Math. Bull., 44:2 (1989), 65–69
37.
S. V. Vostokov, S. O. Gorchinskiy, A. B. Zheglov, Yu. G. Zarkhin, Yu. V. Nesterenko, D. O. Orlov, D. V. Osipov, V. L. Popov, A. G. Sergeev, I. R. Shafarevich, “Aleksei Nikolaevich Parshin (on his 70th birthday)”, Russian Math. Surveys, 68:1 (2013), 189–197
38.
F. A. Bogomolov, Yu. G. Zarhin, Vik. S. Kulikov, Yu. I. Manin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, Yu. G. Prokhorov, M. Reid, I. A. Cheltsov, “Vyacheslav Vladimirovich Shokurov (on his 60th birthday)”, Russian Math. Surveys, 65:6 (2010), 1193–1198
39.
F. A. Bogomolov, Vik. S. Kulikov, Yu. I. Manin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, Yu. G. Prokhorov, A. V. Pukhlikov, M. Reid, I. R. Shafarevich, V. V. Shokurov, “Vasilii Alekseevich Iskovskikh (obituary)”, Russian Math. Surveys, 64:5 (2009), 939–946
40.
V. A. Vassiliev, Yu. G. Zarhin, V. A. Iskovskikh, D. B. Kaledin, Vik. S. Kulikov, Yu. I. Manin, D. O. Orlov, A. N. Parshin, I. R. Shafarevich, “Fedor Alekseevich Bogomolov (on his 60th birthday)”, Russian Math. Surveys, 62:6 (2007), 1233–1237
41.
I. R. Shafarevich, D. O. Orlov, N. A. Tyurin, “Preface”, Proc. Steklov Inst. Math., 246 (2004), 1–2
42.
F. A. Bogomolov, A. L. Gorodentsev, V. A. Iskovskikh, Yu. I. Manin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, V. Ya. Pidstrigach, A. S. Tikhomirov, N. A. Tyurin, I. R. Shafarevich, “Andrei Nikolaevich Tyurin (obituary)”, Russian Math. Surveys, 58:3 (2003), 597–605
Presentations in Math-Net.Ru
1.
Geometric phantom categories Seminar "Complex analysis in several variables" (Vitushkin Seminar) October 31, 2012 16:45
2.
Opening ceremony Annual memorial conference dedicated to the memory of Andrei Nikolaevich Tyurin (24.02.1940–27.10.2002) "Algebraic and Differential Geometry of Andrei Tyurin" October 24, 2012 11:00
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