Fedor A. Bogomolov
New York University
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Primary Section: 11, Mathematics Membership Type:
Member
(elected 2022)
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Biosketch
Fedor Bogomolov is a mathematician recognized for his works in algebraic geometry,algebra and number theory. He is known particularly for his results on the topology of algebraic manifolds, his study of complex manifolds and results on the properties of algebraic curves defined over number fields. Bogomolov was born in Moscow USSR and obtained his bachelors degree from the Moscow State University in 1970. He completed the PhD program in 1973 at the Steklov Institute of Mathematics of the Academy of Science of USSR.He obtained his PhD degree in 1974 after defending his PhD thesis at the Steklov Institute of Mathematics. In 1973 he obtained a position of a researcher at the Steklov Institute and held this position till 1994. In 1994 he joined the Courant Institute of Mathematical Sciences of New York University as a full professor and holds this position currently. He is a member of the National Academy of Sciences and the Academia Europaea.
Research Interests
Fedor Bogomolov is currently working on several problems in algebraic geometry and number theory. He continues his early works on the structure of complex projective manifolds. It invloves the study of algebras of symmetric tensors for vector budnles on such manifolds and also the study of special foliations. Its direction of his work is also related to hyperbolicity problem for projective manifolds. He also continues the study of compact hyperkaler manifolds and in particular of such manifolds having a lagrangian fibration. Another direction of study is related to birational properties of finite group actions on algebraic manifolds and geometric invariants of such actions. This research is also connected naturally to the Galois theory of functional fields. His aim is to understand group theoretic properties of the Sylow subgroups of Galois groups for algebraic closures of functional fields. Another direction of his research has as its aim understanding of the structure of arithmetic points on algebraic curves defined over small fields, i.e number fields and infinite fields. In partucular he is concerned with the study of of unramified correspondences between projective curves defined over such fields. This study is entangled with his study of elliptic curves over number fields and the arithmetic structure of torsion points on such curves.
