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Number Theory, Elimination Theory, Transcendence Theory, Algebraic Geometry, Diophantine Approximations, Metric Number Theory and Diophantine approximation. Other research interests: Arakelov’s Geometry, geometry of numbers, measure and probability theory, ergodic theory, dynamical systems.
Evgeniy Zorin works both in the field of Diophantine approximation and on the theory of transcendental numbers and of algebraic independence. The latter area of research deals with problems of existence of algebraic links between numbers and functions. Classical questions of this type are whether some given real (or complex) numbers are linked by a polynomial relation with integer coefficients. One example of open problems within the area is Schanuel’s conjecture, at the moment proved only in two extreme cases: one is the Lindemann-Weierstrass theorem and another a Fields medal winning result by Alan Baker.
This area of research is strongly intertwined with the theory of Diophantine approximation.