of surfaces of class with ", Bogomolov made the first step in a famously difficult (and still unresolved) problem of classification of surfaces of Kodaira class VII. These are compact complex surfaces with . If they are in addition minimal, they are called class . Kunihiko Kodaira classified all compact complex surfaces except class VII, which are still not understood, except the case (Bogomolov) and (Andrei Teleman, 2005). Other works in arithmetic geometry Bogomolov has contributed to several aspects of arithmetic geometry. He posed the Bogomolov conjecture about small points. Twenty years ago he contributed a proof (among many proofs) of the geometric Szpiro's conjecture which appears to be the nearest to Shinichi Mochizuki's claimed proof of the arithmetic Szpiro conjecture. Later career Bogomolov obtained his Habilitation (Russian "Dr. of Sciences") in 1983. In 1994, he emigrated to the United States and became a full professor at the Courant Institute. He is very active in algebraic geometry and number theory. From 2009 till March 2014 he served as the Editor-in-Chief of the Central European Journal of Mathematics. Since 2014 he serves as the Editor-in-Chief of the European Journal of Mathematics. Since 2010 he is the academic supervisor of the HSE Laboratory of algebraic geometry and its applications. Bogomolov has extensively contributed to the revival of Russian mathematics. 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. References External links Official NYU home page 1946 births 20th-century Russian mathematicians 21st-century Russian mathematicians Living people Soviet mathematicians Academic staff of the Higher School of Economics Courant Institute of Mathematical Sciences faculty Algebraic geometers Moscow State University alumni