Algebraic geometry, derived and noncommutative algebraic geometry, homological algebra, categories of (quasi)coherent sheaves, derived and triangulated categories, mirror symmetry.
Main publications:
D. O. Orlov, “Projective bundles, monoidal transformations, and derived categories of coherent sheaves”, Russian Acad. Sci. Izv. Math., 41:1 (1993), 133–141
D. O. Orlov, “Equivalences of derived categories and K3 surfaces”, Algebraic geometry, 7, J. Math. Sci. (New York), 84:5 (1997), 1361–1381 , arXiv: alg-geom/9606006
D. O. Orlov, “Triangulated Categories of Singularities and D-Branes in Landau–Ginzburg Models”, Proc. Steklov Inst. Math., 246 (2004), 227–248 , arXiv: math/0302304
D. Orlov, “Derived categories of coherent sheaves and triangulated categories of singularities”, Algebra, arithmetic, and geometry, v. II, Progr. Math., 270, Birkhäuser Boston, Inc., 2009, 503–531 , arXiv: math/0503632
V. A. Lunts, D. O. Orlov, “Uniqueness of enhancement for triangulated categories”, J. Amer. Math. Soc., 23:3 (2010), 853–908 , arXiv: 0908.4187
S. Gorchinskiy, D. Orlov, “Geometric phantom categories”, Publ. Math. Inst. Hautes Études Sci., 117:1 (2013), 329–349 , arXiv: 1209.6183
Dmitri Orlov, “Smooth and proper noncommutative schemes and gluing of DG categories”, Adv. Math., 302 (2016), 59–105 , arXiv: 1402.7364
Dmitri Orlov, “Finite-dimensional differential graded algebras and their geometric realizations”, Adv. Math., 366 (2020), 107096 , 33 pp., arXiv: 1907.08162
D. Orlov, Twisted tensor product, smooth DG algebras, and noncommutative resolutions of singular curves, 2024 , 27 pp., Dedicated to the blessed memory of Ludwig Dmitrievich Faddeev on the occasion of his 90th birthday, arXiv: 2405.04738
2.
D. O. Orlov, “Skruchennoe tenzornoe proizvedenie, gladkie DG algebry i nekommutativnye razresheniya osobykh krivykh”, Funkts. analiz i ego pril., 58:4 (2024) (to appear) ; (to appear)
3.
N. N. Andreev, S. E. Boichenko, S. O. Gorchinskiy, V. V. Kozlov, N. Yu. Lukoyanov, D. K. Mamii, D. O. Orlov, A. M. Raigorodskii, “The Third Conference of Russian Mathematical Centers”, Russian Math. Surveys, 79:1 (2024), 183–187
4.
N. N. Andreev, M. A. Vsemirnov, S. O. Gorchinskiy, D. N. Zaporozhets, S. V. Kislyakov, V. V. Kozlov, M. A. Korolev, D. O. Orlov, Yu. S. Osipov, D. V. Treschev, P. A. Yaskov, “Steklov Institute – 90!”, Russian Math. Surveys, 79:3 (2024), 557–562
5.
S. O. Gorchinskiy, V. G. Danilov, S. Yu. Dobrokhotov, V. V. Kozlov, V. E. Nazaikinskii, N. N. Nefedov, D. O. Orlov, S. A. Stepin, I. A. Taimanov, D. V. Treschev, N. A. Tyurin, A. T. Fomenko, S. E. Yakush, “Andrei Igorevich Shafarevich (on his sixtieth birthday)”, Russian Math. Surveys, 79:3 (2024), 553–556
6.
A. I. Aptekarev, S. I. Bezrodnykh, M. A. Guzev, S. I. Kabanikhin, B. S. Kashin, S. V. Kislyakov, V. V. Kozlov, N. Yu. Lukoyanov, M. B. Markov, D. O. Orlov, Yu. S. Osipov, I. B. Petrov, V. P. Platonov, I. A. Taimanov, V. F. Tishkin, D. V. Treschev, E. E. Tyrtyshnikov, M. V. Iakobovski, “Boris Nikolaevich Chetverushkin (on his eightieth birthday)”, Uspekhi Mat. Nauk, 79:4(478) (2024), 181–187
2023
7.
D. O. Orlov, “Smooth DG algebras and twisted tensor product”, UMN, 78:5(473) (2023), 65–92 , arXiv: 2305.19799
F. A. Bogomolov, A. M. Vershik, S. V. Vostokov, S. O. Gorchinskiy, A. B. Zheglov, Yu. G. Zarhin, S. V. Konyagin, Vik. S. Kulikov, Yu. V. Nesterenko, D. O. Orlov, D. V. Osipov, I. A. Panin, V. P. Platonov, V. L. Popov, Yu. G. Prokhorov, A. L. Smirnov, “Alexey Nikolaevich Parshin (obituary)”, Russian Math. Surveys, 78:3 (2023), 549–554
9.
S. O. Gorchinskiy, Vik. S. Kulikov, V. V. Nikulin, D. O. Orlov, D. V. Osipov, V. L. Popov, N. A. Tyurin, G. B. Shabat, A. I. Shafarevich, V. V. Shokurov, “Igor Rostislavovich Shafarevich (on the centenary of his birthday)”, Russian Math. Surveys, 78:6 (2023), 1167–1178
2022
10.
F. A. Bogomolov, S. O. Gorchinskiy, A. B. Zheglov, V. V. Nikulin, D. O. Orlov, D. V. Osipov, A. N. Parshin, V. L. Popov, V. V. Przyjalkowski, Yu. G. Prokhorov, M. Reid, A. G. Sergeev, D. V. Treschev, A. K. Tsikh, I. A. Cheltsov, E. M. Chirka, “Viktor Stepanovich Kulikov (on his 70th birthday)”, Russian Math. Surveys, 77:3 (2022), 555–557
11.
A. A. Agrachev, R. V. Gamkrelidze, V. V. Kozlov, Yu. I. Zhuravlev, A. V. Mikhalev, A. V. Ovchinnikov, D. O. Orlov, V. L. Popov, V. G. Romanov, A. L. Semenov, V. G. Chirskii, V. A. Shamolin, “To the 55th anniversary of Professor M. V. Shamolin”, Geometry, Mechanics, and Differential Equations, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 210, VINITI, Moscow, 2022, 3–5
2021
12.
A. G. Kuznetsov, D. O. Orlov, N. A. Tyurin, A. L. Gorodentsev, “Collective obituary. Sergey A. Kuleshov (24.12.1962 – 15.05.2021)”, Math. Ed., 2021, no. 2(98), 2–4
13.
D. O. Orlov, “Twisted tensor products of DG algebras”, Russian Math. Surveys, 76:6 (2021), 1146–1148
14.
V. A. Alexeev, C. Birkar, F. A. Bogomolov, Yu. G. Zarhin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, Yu. G. Prokhorov, M. Reid, A. S. Tikhomirov, I. A. Cheltsov, “Vyacheslav Vladimirovich Shokurov (on his 70th birthday)”, Russian Math. Surveys, 76:3 (2021), 553–556
15.
A. I. Shafarevich, V. N. Chubarikov, D. O. Orlov, A. O. Ivanov, A. V. Mikhalev, V. G. Chirskii, A. Yu. Ol'shanskii, M. V. Zaicev, I. B. Kozhukhov, A. Ya. Kanel-Belov, N. M. Dobrovol'skii, N. N. Dobrovol'skii, I. Yu. Rebrova, I. N. Balaba, “In memory of Vyacheslav Alexandrovich Artamonov”, Chebyshevskii Sb., 22:5 (2021), 417–418
2020
16.
Dmitri Orlov, “Finite-dimensional differential graded algebras and their geometric realizations”, Adv. Math., 366 (2020), 107096 , 33 pp., arXiv: 1907.08162
S. I. Adian, V. M. Buchstaber, E. I. Zelmanov, S. V. Kislyakov, V. V. Kozlov, Yu. V. Matiyasevich, S. P. Novikov, D. O. Orlov, A. N. Parshin, V. L. Popov, D. V. Treschev, “Vladimir Petrovich Platonov (on his 80th birthday)”, Russian Math. Surveys, 75:2 (2020), 387–391
18.
S. V. Bolotin, A. V. Borisov, A. V. Karapetyan, B. S. Kashin, E. I. Kugushev, A. I. Neishtadt, D. O. Orlov, D. V. Treschev, “Valerii Vasil'evich Kozlov (on his 70th birthday)”, Russian Math. Surveys, 75:6 (2020), 1165–1180
2019
19.
L. A. Borisov, D. O. Orlov, “Equivariant exceptional collections on smooth toric stacks”, Izv. Math., 83:4 (2019), 698–730
20.
D. O. Orlov, “Finite-dimensional DG algebras and their properties”, Russian Math. Surveys, 74:4 (2019), 764–766
21.
V. A. Artamonov, V. M. Buchstaber, È. B. Vinberg, L. V. Kuz'min, V. S. Kulikov, V. N. Latyshev, A. V. Mikhalev, A. Yu. Ol'shanskii, D. O. Orlov, A. N. Parshin, D. I. Piontkovskii, “Evgenii Solomonovich Golod (obituary)”, Russian Math. Surveys, 74:5 (2019), 927–933
22.
V. A. Alexandrov, L. D. Beklemishev, V. M. Buchstaber, A. Yu. Vesnin, A. A. Gaifullin, N. P. Dolbilin, N. Yu. Erokhovets, M. D. Kovalev, V. S. Makarov, S. P. Novikov, D. O. Orlov, A. N. Parshin, I. Kh. Sabitov, D. V. Treschev, O. K. Sheinman, E. V. Shchepin, “Mikhail Ivanovich Shtogrin (on his 80th birthday)”, Russian Math. Surveys, 74:6 (2019), 1159–1162
2018
23.
D. O. Orlov, “Derived noncommutative schemes, geometric realizations, and finite dimensional algebras”, Russian Math. Surveys, 73:5 (2018), 865–918 , arXiv: 1808.02287
24.
A. A. Beilinson, A. S. Vishik, D. A. Kazhdan, M. M. Kapranov, A. S. Merkurjev, D. O. Orlov, I. A. Panin, A. A. Suslin, N. A. Tyurin, G. B. Shabat, “Vladimir Aleksandrovich Voevodsky (obituary)”, Russian Math. Surveys, 73:3 (2018), 519–531
25.
I. V. Arzhantsev, V. M. Buchstaber, L. V. Kuz'min, V. S. Kulikov, A. Yu. Ol'shanskii, D. O. Orlov, A. N. Parshin, D. I. Piontkovskii, Yu. G. Prokhorov, “Evgenii Solomonovich Golod”, Chebyshevskii Sb., 19:2 (2018), 542–545
2016
26.
Dmitri Orlov, “Smooth and proper noncommutative schemes and gluing of DG categories”, Adv. Math., 302 (2016), 59–105 , arXiv: 1402.7364
D. O. Orlov, “Gluing of categories and Krull–Schmidt partners”, Russian Math. Surveys, 71:3 (2016), 594–596 , arXiv: 1606.00332
28.
Sovremennye problemy matematiki, mekhaniki i matematicheskoi fiziki. II, Sbornik statei, Trudy MIAN, 294, ed. D. O. Orlov, A. G. Sergeev, MAIK «Nauka/Interperiodika», M., 2016 , 327 pp.
29.
V. M. Buchstaber, S. M. Gusein-Zade, M. È. Kazarian, V. V. Kozlov, S. K. Lando, S. P. Novikov, D. O. Orlov, A. G. Khovanskii, “Viktor Anatolevich Vassiliev (on his 60th birthday)”, Russian Math. Surveys, 71:6 (2016), 1153–1157
2015
30.
D. O. Orlov, “Geometric Realizations of Quiver Algebras”, Proc. Steklov Inst. Math., 290 (2015), 70–83 , arXiv: 1503.03174
31.
Sovremennye problemy matematiki, mekhaniki i matematicheskoi fiziki, Sbornik statei, Trudy MIAN, 290, ed. D. O. Orlov, A. G. Sergeev, MAIK «Nauka/Interperiodika», M., 2015 , 343 pp.
2013
32.
A. Canonaco, D. Orlov, P. Stellari, “Does full imply faithful?”, J. Noncommut. Geom., 7:2 (2013), 357–371 , arXiv: 1101.5931
M. Abouzaid, D. Auroux, A. I. Efimov, L. Katzarkov, D. Orlov, “Homological mirror symmetry for punctured spheres”, J. Amer. Math. Soc., 26:4 (2013), 1051–1083 , arXiv: 1103.4322
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
2012
37.
D. Orlov, “Matrix factorizations for nonaffine LG-models”, Math. Ann., 353:1 (2012), 95–108 , arXiv: 1101.4051
D. Orlov, “Landau–Ginzburg models, D-branes, and Mirror Symmetry”, Matemática Contemporânea, 41 (2012), 75–112 , arXiv: 1111.2962
2011
39.
D. Orlov, “Formal completions and idempotent completions of triangulated categories of singularities”, Adv. Math., 226:1 (2011), 206–217 , arXiv: 0901.1859
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
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
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
2009
44.
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
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
D. Orlov, “Derived categories of coherent sheaves and triangulated categories of singularities”, Algebra, arithmetic, and geometry, v. II, Progr. Math., 270, Birkhäuser Boston, Inc., 2009, 503–531 , arXiv: math/0503632
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
2008
49.
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 , arXiv: math/0404281
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 , arXiv: math/0101023
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
2006
52.
D. Auroux, L. Katzarkov, D. Orlov, “Mirror symmetry for del Pezzo surfaces: vanishing cycles and coherent sheaves”, Invent. Math., 166:3 (2006), 537–582 , arXiv: math/0506166
D. O. Orlov, “Triangulated categories of singularities and equivalences between Landau–Ginzburg models”, Sb. Math., 197:12 (2006), 1827–1840 , arXiv: math/0503630
2005
54.
D. O. Orlov, “Derived categories of coherent sheaves and motives”, Russian Math. Surveys, 60:6 (2005), 1242–1244 , arXiv: math/0512620
2004
55.
A. N. Kapustin, D. O. Orlov, “Lectures on mirror symmetry, derived categories, and D-branes”, Russian Math. Surveys, 59:5 (2004), 907–940 , arXiv: math/0308173
56.
D. O. Orlov, “Triangulated Categories of Singularities and D-Branes in Landau–Ginzburg Models”, Proc. Steklov Inst. Math., 246 (2004), 227–248 , arXiv: math/0302304
57.
I. R. Shafarevich, D. O. Orlov, N. A. Tyurin, “Preface”, Proc. Steklov Inst. Math., 246 (2004), 1–2
2003
58.
A. Kapustin, D. Orlov, “Remarks on A-branes, mirror symmetry, and the Fukaya category”, J. Geom. Phys., 48:1 (2003), 84–99 , arXiv: hep-th/0109098
A. Kapustin, D. Orlov, “Vertex algebras, mirror symmetry, and D-branes: the case of complex tori”, Comm. Math. Phys., 233:1 (2003), 79–136 , arXiv: hep-th/0010293
D. O. Orlov, “Quasi-coherent sheaves in commutative and non-commutative geometry”, Izv. Math., 67:3 (2003), 535–554
61.
D. O. Orlov, “Derived categories of coherent sheaves and equivalences between them”, Russian Math. Surveys, 58:3 (2003), 511–591
62.
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
2002
63.
A. Bondal, D. Orlov, “Derived categories of coherent sheaves”, Proceedings of the International Congress of Mathematicians (Beijing, 2002), v. II, Higher Ed. Press, Beijing, 2002, 47–56 , arXiv: math/0206295
64.
D. O. Orlov, “Derived categories of coherent sheaves on Abelian varieties and equivalences between them”, Izv. Math., 66:3 (2002), 569–594 , arXiv: alg-geom/9712017
2001
65.
A. Kapustin, A. Kuznetsov, D. Orlov, “Noncommutative instantons and twistor transform”, Comm. Math. Phys., 221:2 (2001), 385–432 , arXiv: hep-th/0002193
D. O. Orlov, “Equivalences of derived categories and K3 surfaces”, Algebraic geometry, 7, J. Math. Sci. (New York), 84:5 (1997), 1361–1381 , arXiv: alg-geom/9606006
S. A. Kuleshov, D. O. Orlov, “Exceptional sheaves on del Pezzo surfaces”, Russian Acad. Sci. Izv. Math., 44:3 (1995), 479–513
1993
71.
D. O. Orlov, “Projective bundles, monoidal transformations, and derived categories of coherent sheaves”, Russian Acad. Sci. Izv. Math., 41:1 (1993), 133–141
1991
72.
D. O. Orlov, “Exceptional set of vector bundles on the variety $V_5$”, Moscow Univ. Math. Bull., 46:5 (1991), 48–50
1989
73.
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
Открытие D. O. Orlov Conference on algebra, algebraic geometry, and number theory on the
occasion of academician Igor Rostislavovich Shafarevich 100th birthday June 5, 2023 10:50
15.
Конечномерные ДГ алгебры и их свойства D. O. Orlov “Numbers and functions” – Memorial conference for 80th birthday of Alexey Nikolaevich Parshin November 28, 2022 16:40
16.
Гипотеза Морделла. Семинар 2 D. O. Orlov Summer School “Contemporary Mathematics” Named After Vitaly Arnold, 2022 July 23, 2022 17:15
17.
Гипотеза Морделла. Лекция 1 D. O. Orlov Summer School “Contemporary Mathematics” Named After Vitaly Arnold, 2022 July 21, 2022 17:15
Семинар 6. Алгебраическая геометрия D. O. Orlov, Yu. G. Prokhorov, C. A. Shramov Seminar by D. O. Orlov, Yu. G. Prokhorov and C. A. Shramov "Algebraic geometry" March 18, 2020 16:00
25.
Семинар 5. Алгебраическая геометрия D. O. Orlov, Yu. G. Prokhorov, C. A. Shramov Seminar by D. O. Orlov, Yu. G. Prokhorov and C. A. Shramov "Algebraic geometry" March 11, 2020 16:00
26.
Семинар 4. Алгебраическая геометрия D. O. Orlov, Yu. G. Prokhorov, C. A. Shramov Seminar by D. O. Orlov, Yu. G. Prokhorov and C. A. Shramov "Algebraic geometry" March 4, 2020 16:00
27.
Семинар 3. Алгебраическая геометрия D. O. Orlov, Yu. G. Prokhorov, C. A. Shramov Seminar by D. O. Orlov, Yu. G. Prokhorov and C. A. Shramov "Algebraic geometry" February 26, 2020 16:00
28.
Семинар 2. Алгебраическая геометрия D. O. Orlov, Yu. G. Prokhorov, C. A. Shramov Seminar by D. O. Orlov, Yu. G. Prokhorov and C. A. Shramov "Algebraic geometry" February 19, 2020 16:00
29.
Семинар 1. Алгебраическая геометрия D. O. Orlov, Yu. G. Prokhorov, C. A. Shramov Seminar by D. O. Orlov, Yu. G. Prokhorov and C. A. Shramov "Algebraic geometry" February 12, 2020 16:00
Geometric realisations of algebraic objects D. O. Orlov International conference ''Algebra, algebraic geometry and number theory'' dedicated to the memory of academician Igor Rostislavovich Shafarevich June 13, 2018 16:20
Geometric phantom categories D. O. Orlov Seminar "Complex analysis in several variables" (Vitushkin Seminar) October 31, 2012 16:45
75.
Opening ceremony D. O. Orlov 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
Open ceremony D. O. Orlov, A. G. Sergeev, A. N. Parshin, M. Reid, V. V. Shokurov International conference "Geometry of Algebraic Varieties" dedicated to the memory of Vasily Alexeevich Iskovskikh June 29, 2009 10:00
Mirror symmetry from the mathematical point of view Dmitry Orlov General Mathematics Seminar of the St. Petersburg Division of Steklov Institute of Mathematics, Russian Academy of Sciences October 9, 2006
Modern problems of mathematics, mechanics, and mathematical physics. II, Collected papers, Trudy Mat. Inst. Steklova, 294, ed. D. O. Orlov, A. G. Sergeev, 2016, 327 с. http://mi.mathnet.ru/book1618
Modern problems of mathematics, mechanics, and mathematical physics, Collected papers, Trudy Mat. Inst. Steklova, 290, ed. D. O. Orlov, A. G. Sergeev, 2015, 343 с. http://mi.mathnet.ru/book1589