Dmitri Olegovich Orlov – Wikipedia

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Russian mathematician

Dmitri Olegovich Orlov, (Дмитрий Олегович Орлов, born September 19, 1966 in Vladimir, Russia) is a Russian mathematician, specializing in algebraic geometry. He is known for the Bondal-Orlov reconstruction theorem (2001).[1]

Education and career[edit]

In 1988 Orlov graduated from the Faculty of Mechanics and Mathematics of Moscow State University. There he received his Candidate of Sciences degree (PhD) 1991 with thesis Производные категории когерентных пучков, моноидальные преобразования и многообразия Фано (Derived categories of coherent sheaves, monoidal transformations and Fano varieties) under Vasilii Alekseevich Iskovskikh (and Alexey Igorevich Bondal).[2]
At the Steklov Institute of Mathematics, Orlov was from April 1996 to April 2011 a researcher in the Algebra Department and is since April 2011 the head of the Algebraic Geometry Department.[3] In 2002 Orlov received his Doctor of Sciences degree (habilitation) with thesis Производные категории когерентных пучков и эквивалентности между ними (Derived categories of coherent sheaves and equivalences between them).[4] In 2002 he was, with A. Bondal, an Invited Speaker with talk Derived categories of coherent sheaves at the International Congress of Mathematicians in Beijing.[5]

Orlov’s research deals with homological algebra, (derived categories, triangulated categories), algebraic geometry (derived algebraic geometry, homological mirror symmetry, quasicoherent sheaves, and noncommutative geometry.[6]

Orlov is one of the pioneers of the modern emerging categorical framework which unites the commutative and noncommutative algebraic geometry, via the study of enhanced triangulated categories of quasicoherent sheaves.[7]

He was elected on December 20, 2011 a corresponding member and on 15 November 2019 a full member of the Russian Academy of Sciences.[citation needed]

Selected publications[edit]

  • with A. Bondal: Semi-orthogonal decomposition for algebraic varieties, Arxiv, 1995
  • with A. Bondal: Reconstruction of a variety from the derived category and groups of autoequivalences, Compositio Math., vol. 125, 2001, pp. 327–344, Arxiv
  • with A. I. Bondal: Derived categories of coherent sheaves, Proc. Internat. Congress of Mathematicians, Peking, 2002, Arxiv
  • Quasi-coherent sheaves in commutative and non-commutative geometry, Izv. RAN. Ser. Mat., vol. 67, 2003, pp. 119–138
  • Derived categories of coherent sheaves and equivalences between them, Russian Mathematical Surveys, vol. 58, 2003, p. 511
  • with A. N. Kapustin: Lectures on mirror symmetry, derived categories, and D-branes, Russian Mathematical Surveys, vol. 59, 2004, pp. 907–940, Arxiv
  • Derived categories of coherent sheaves and motives, Russian Mathematical Surveys, vol. 60, 2005, pp. 1242–1244, Arxiv
  • with V. A. Lunts, A. I. Efimov: Deformation theory of objects in homotopy and derived categories, Part 1, Advances in Mathematics, vol. 222, 2009, pp. 359–401, Arxiv, Part 2, Advances in Mathematics, vol. 224, 2010, pp. 45–102, Arxiv, Part 3, Advances in Mathematics, vol. 226, 2011, pp. 3857–3911, Arxiv
  • with Valery A. Lunts: Uniqueness of enhancement for triangulated categories, J. Amer. Math. Soc., vol. 23, 2010, pp. 853–908, doi:10.1090/S0894-0347-10-00664-8 Arxiv
  • Formal completions and idempotent completions of triangulated categories of singularities, Advances in Mathematics, vol. 226, 2011, pp. 206–217, Arxiv
  • Landau-Ginzburg Models, D-branes, and Mirror Symmetry, Mat. Contemp., vol. 41, 2012, pp. 75–112, Arxiv
  • with Mohammed Abouzaid, Denis Auroux, Alexander I. Efimov, and Ludmil Katzarkov: Homological mirror symmetry for punctured spheres, J. Amer. Math. Soc. vol. 26, 2013, pp. 1051-1083 doi:10.1090/S0894-0347-2013-00770-5
  • Derived noncommutative schemes, geometric realizations, and finite dimensional algebras, Russian Math. Surveys, vol. 73, 2018, pp. 865–918, Arxiv

References[edit]

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