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

personal data
SURNAME	Bondal, Alexei Igorevich
ALTERNATIVE NAMES	Бондал, Алексей Игоревич (Russian)
BRIEF DESCRIPTION	Russian mathematician
DATE OF BIRTH	20th century

[1] Alexei Igorewitsch Bondal in the Mathematics Genealogy Project (English)

[2] t-Lab on Bondal