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
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
4.
D. O. Orlov, “Twisted tensor products of DG algebras”, Russian Math. Surveys, 76:6 (2021), 1146–1148
5.
Dmitri Orlov, “Finite-dimensional differential graded algebras and their geometric realizations”, Adv. Math., 366 (2020), 107096 , 33 pp., arXiv: 1907.08162
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
D. Orlov, “Landau–Ginzburg models, D-branes, and Mirror Symmetry”, Matemática Contemporânea, 41 (2012), 75–112 , arXiv: 1111.2962
18.
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
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
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
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
30.
D. O. Orlov, “Derived categories of coherent sheaves and motives”, Russian Math. Surveys, 60:6 (2005), 1242–1244 , arXiv: math/0512620
31.
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
32.
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
33.
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
36.
D. O. Orlov, “Derived categories of coherent sheaves and equivalences between them”, Russian Math. Surveys, 58:3 (2003), 511–591
37.
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
38.
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
39.
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
44.
D. O. Orlov, “Projective bundles, monoidal transformations, and derived categories of coherent sheaves”, Russian Acad. Sci. Izv. Math., 41:1 (1993), 133–141
45.
D. O. Orlov, “Exceptional set of vector bundles on the variety $V_5$”, Moscow Univ. Math. Bull., 46:5 (1991), 48–50
46.
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
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
Information matherials
49.
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
50.
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
51.
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
52.
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
Personalia
53.
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
54.
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
55.
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
56.
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
57.
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
58.
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
59.
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
60.
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
61.
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
62.
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
63.
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
64.
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
65.
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
66.
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
67.
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
68.
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
69.
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
70.
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
Miscellaneous
71.
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.
72.
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.
73.
I. R. Shafarevich, D. O. Orlov, N. A. Tyurin, “Preface”, Proc. Steklov Inst. Math., 246 (2004), 1–2;
Presentations in Math-Net.Ru
1.
TBA Dmitri Orlov Sino-Russian Interdisciplinary Mathematical Conference-2 November 26, 2024 16:00
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
22.
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
23.
Гипотеза Морделла. Семинар 2 D. O. Orlov Summer School “Contemporary Mathematics” Named After Vitaly Arnold, 2022 July 23, 2022 17:15
24.
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
32.
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
33.
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
34.
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
35.
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
36.
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
82.
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