Algebraic geometry, homological algebra, noncommutative algebraic geometry, categories of coherent sheaves on algebraic varieties, derived and triangulated categories, mirror symmetry.
Main publications
Orlov D., “Proektivnye rassloeniya, monoidalnye preobrazovaniya i proizvodnye kategorii kogerentnykh puchkov”, Izv RAN. Ser. matem., 56:4 (1992), 852–862
Orlov D., “Equivalences of derived categories and K3 surfaces”, J. Math. Sci. (New York), 84:5 (1997), 1361–1381
Bondal A., Orlov D., “Reconstruction of a variety from the derived category and groups of autoequivalences”, Compositio Mathematica, 125:3 (2001), 327–344
Orlov D., “Derived categories of coherent sheaves and equivalences between them”, Uspekhi Mat. Nauk, 58
yr 2003:3(351), 89–172 (Russian) ; Engl. transl.: Russian Math. Surveys, 58:3 (2003), 511–591
Orlov D., “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., 2004, no. 3 (246), 227–248
Vasilii Alekseevich Iskovskikh (obituary) 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 Uspekhi Mat. Nauk, 2009, 64:5(389), 167–174
12.
Fedor Alekseevich Bogomolov (on his 60th birthday) 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 Uspekhi Mat. Nauk, 2007, 62:6(378), 193–197
13.
Preface I. R. Shafarevich, D. O. Orlov, N. A. Tyurin Tr. Mat. Inst. Steklova, 2004, 246, 7–9
14.
Andrei Nikolaevich Tyurin (obituary) 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 Uspekhi Mat. Nauk, 2003, 58:3(351), 176–182
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