Alexei Igorevich Bondal
Alexei Igorewitsch Bondal ( Russian Алексей Игоревич Бондал ) is a Russian mathematician who studies algebra and algebraic geometry .
life and work
Bondal received his doctorate in 1989 from Lomonossow University under Alexei Ivanovich Kostrikin . In 2005 he completed his habilitation ( Russian doctorate ). He is at the Steklov Institute in Moscow.
With Michail Michailowitsch Kapranow, Bondal is a pioneer in the treatment of classical algebraic geometry via homological algebra, more precisely derived categories of coherent sheaves based on algebraic varieties ( derivative algebraic geometry ). He also influenced the formulation of the role of derived categories in the mirror symmetry of algebraic varieties (homological mirror symmetry) by Maxim Lwowitsch Konzewitsch . With Dmitri Olegowitsch Orlow , he gave conditions for the reconstruction of algebraic varieties from the derived category. He also dealt with the application of derived categories in the classification program of higher-dimensional algebraic varieties ( Minimal Model Program ) by Shigefumi Mori and formulated assumptions about their behavior in flip and flop transformations (partial results were obtained by Tom Bridgeland and Yūjirō Kawamata ). He also pursues application in non-commutative algebraic geometry.
He was invited speaker at the 2002 International Congress of Mathematicians in Beijing (Derived Categories of coherent sheaves, with Dmitri Orlov)
Fonts
- with Michel Van den Bergh Generators and representability of functors in commutative and noncommutative geometry , Mosc. Math. J., Volume 3, 2003, pp. 1-36
- with Michail Kapranov Enhanced triangulated categories , Math. USSR-Sbornik, 70, 1991, 93-107
- with Kapranov Representable functors, Serre functors, and mutations , Math. USSR-Izvestija, 35, 1990, 519-541
- with Dmitri Orlov Reconstruction of a variety from the derived category and groups of autoequivalences , Compositio Math., 125, 2001, 327-344
- From Algebras to Varieties, IPMU News, 2005, pdf
literature
- Raphaël Rouquier: Catégories dérivées et géométrie birationnelle, d'après Bondal, Orlov, Bridgeland, Kawamata…, Seminaire Bourbaki 946, 2004/05
Web links
Individual evidence
- ↑ Alexei Igorewitsch Bondal in the Mathematics Genealogy Project (English)
- ↑ ncat-Lab on Bondal
personal data | |
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SURNAME | Bondal, Alexei Igorevich |
ALTERNATIVE NAMES | Бондал, Алексей Игоревич (Russian) |
BRIEF DESCRIPTION | Russian mathematician |
DATE OF BIRTH | 20th century |