Alexey Parshin - Curriculum Vitae#

Education and career:

Graduated in 1964 from the Faculty of Mathematics and Mechanics of Moscow State University.
Graduate student at the Steklov Institute of Mathematics, PhD received in 1968.
Russian doctorate of sciences (Doctor Nauk) recieved in 1983.

Scientific researcher at Steklov Mathematical Institute of RAS since 1968.
Head of the Department of Algebra since 1995.

Main results:

1) Definition of iterated integrals on manifolds (independently of K. T. Chen).
2) Proof of Shafarevich finiteness conjecture for curves with fixed genus, base function field, and the set of points of bad (potentially good) reduction.
3) Proof of the fact that Shafarevich finiteness conjecture implies Mordell finiteness conjecture for curves defined over any global field.
4) Construction of n-dimensional local fields and adelic groups with applications to the residue theory, theory of vector bundles (Serre duality, Chern classes, Lefschetz formula), class field theory (using algebraic K-theory) and harmonic analysis on algebraic and arithmetic surfaces (Fourier transform and Poisson formula).
5) Formulation of the Bogomolov-Miyaoka type inequality for the Chern classes of arithmetic surfaces. Proof of the fact that this implies among others effective Mordell conjecture and Szpiro inequality.
6) Generalization of Kadomtsev-Petviashvili integrable system to the case of n variables. Proof of the fact that there exist infinitely many conservation laws.
7) Classification of irreducible infinite-dimensional representations of discrete finitely generated Heisenberg groups. Proof of modularity of the characters for these representations.
8) Study of automorphic induction and base change for morphisms of algebraic surfaces onto algebraic curves.

Publications:

More than 50 scientific publications.
A full list of publications