Fedor Bogomolov

Fedor Alekseyevich Bogomolov (born 26 September 1946) (Фёдор Алексеевич Богомолов) is a Russian and American mathematician, known for his research in algebraic geometry and number theory.

In his early papers[1][2][3] Bogomolov studied the manifolds which were later called Calabi–Yau and hyperkähler.

He proved a decomposition theorem, used for the classification of manifolds with trivial canonical class.

It has been re-proven using the Calabi–Yau theorem and Berger's classification of Riemannian holonomies, and is foundational for modern string theory.

In the late 1970s and early 1980s Bogomolov studied the deformation theory for manifolds with trivial canonical class.

While studying the deformation theory of hyperkähler manifolds, Bogomolov discovered what is now known as the Bogomolov–Beauville–Fujiki form on

Studying properties of this form, Bogomolov erroneously concluded that compact hyperkaehler manifolds do not exist, with the exception of K3 surfaces, tori, and their products.

Bogomolov's paper on "Holomorphic tensors and vector bundles on projective manifolds" proves what is now known as the Bogomolov–Miyaoka–Yau inequality, and also proves that a stable bundle on a surface, restricted to a curve of sufficiently big degree, remains stable.

In "Families of curves on a surface of general type",[6] Bogomolov laid the foundations to the now popular approach to the theory of diophantine equations through geometry of hyperbolic manifolds and dynamical systems.

Some 25 years later, Michael McQuillan[7] extended this argument to prove the famous Green–Griffiths conjecture for such surfaces.

",[8] Bogomolov made the first step in a famously difficult (and still unresolved) problem of classification of surfaces of Kodaira class VII.

From 2009 till March 2014 he served as the Editor-in-Chief of the Central European Journal of Mathematics.

[10] Since 2010 he is the academic supervisor of the HSE Laboratory of algebraic geometry and its applications.

Three major international conferences commemorating his 70th birthday were held in 2016: at the Courant Institute, the University of Nottingham, and the Higher School of Economics in Moscow.