Ivan Fesenko
| Ivan Fesenko | |
|---|---|
| Born | St Petersburg, Russia |
| Fields | Mathematician |
| Institutions | University of Nottingham |
| Alma mater | Saint Petersburg State University |
| Doctoral advisor | Sergei V. Vostokov |
| Doctoral students | Caucher Birkar, Alexander Stasinski, Matthew Morrow |
| Known for | higher number theory, higher class field theory, arithmetic zeta functions, higher translation invariant measure and integration, higher adeles, higher zeta integrals, higher Tate-Iwasawa theory, higher adelic structures, Fesenko group |
| Notable awards | Petersburg Mathematical Society Prize |
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Website https://www.maths.nottingham.ac.uk/personal/ibf/ |
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Ivan Borisovich Fesenko (Russian: Иван Борисович Фесенко; born 1962) is a mathematician working in number theory.
In 1979 Ivan Fesenko was the winner of All-Russian mathematical olympiad. He got his PhD in St Petersburg University and worked at St Petersburg University since 1986. He was awarded a number of prizes including the Prize of the Petersburg Mathematical Society. Since 1995 he is professor in pure mathematics at University of Nottingham. Since 2015 he is the principal investigator of a research team of Universities of Nottingham and Oxford supported by EPSRC Programme Grant on Symmetries and Correspondences and intra-disciplinary developments.
Ivan Fesenko has contributed to number theory, algebraic K-theory, infinite group theory, measure and integration theory. In number theory he played a fundamental role in explicit reciprocity formulas, class field theories, higher local fields, higher class field theories, higher adelic structures, higher zeta integrals, arithmetic zeta functions, and other areas. He is a coauthor of a textbook on local fields and a coeditor of a volume on higher local fields.
Fesenko discovered several types of explicit formulas for the generalized Hilbert symbol on local fields and higher local fields, which belong to the branch of Vostokov's explicit formulas. He developed several generalizations of class field theory. He extended the explicit method of Jürgen Neukirch in class field theory in various directions, to deal with generalized class formations which do not satisfy the property of Galois descent. Together with Kazuya Kato, he is the main contributor to higher local class field theory. This theory uses Milnor K-groups instead of the multiplicative group of a usual local field with finite residue field. He constructed explicit p-class field theory for local fields with perfect and imperfect residue field where indices of norm groups can be infinite. In 2000 he initiated "noncommutative local class field theory" for arithmetically profinite Galois extensions of local fields. This arithmetic theory can be viewed as an alternative to the representation theoretical local Langlands correspondence.
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