Ravi Ramakrishna

Professor of Mathematics
595 Malott Hall
(607) 255-3473
ravi@math.cornell.edu

Ph.D. (1992) Princeton University

Research Area

Algebraic number theory

My research is in Galois theory. This is the branch of mathematics concerned with symmetries of solutions of equations. There is an object that encodes all symmetries of solutions to all equations, the absolute Galois group of the rational numbers. I study this object and its relations with number theory. The study of these symmetries has gained an increasingly important role in number theory in recent years. In particular, Galois theory played an important role in the solution of Fermat's Last Theorem.

Selected Publications

Deforming Galois representations and the conjectures of Serre and Fontaine-Mazur, Ann. of Math. (2) 156 no. 1 (2002), 115–154.

Deformations of certain reducible Galois representations, J. Ramanujan Math. Soc. 17 no. 1 (2002), 51–63.

Finitenss of Selmer groups and deformation rings, Invent. Math. 154 (2003), 179–198.

Transcendental $\ell$-adic Galois representations (with C. Khare and M. Larsen), Math Research Letters 12 (2005), 685–700.

Constructing semisimple p-adic Galois representations with prescribed properties (with C. Khare and M. Larsen), American Journal of Mathematics 127 (2005), 709–734.