Ivan Fesenko is a mathematician working in number theory and its interaction with other areas of modern mathematics.
[pub 12] The second development is an application to the generalized Riemann hypothesis, which in this higher theory is reduced to a certain positivity property of small derivatives of the boundary function and to the properties of the spectrum of the Laplace transform of the boundary function.
[pub 13][pub 14] [4] The third development is a higher adelic study of relations between the arithmetic and analytic ranks of an elliptic curve over a global field, which in conjectural form are stated in the Birch and Swinnerton-Dyer conjecture for the zeta function of elliptic surfaces.
[pub 17] His contributions include his analysis of class field theories and their main generalizations.
Fesenko played an active role in organizing the study of inter-universal Teichmüller theory of Shinichi Mochizuki.