Alvaro Lozano-Robledo

H. C. Wang Assistant Professor of Mathematics

Web Site www.math.cornell.edu/~alozano Contact Information Office:  584 Malott Hall Phone:  (607) 255-4738 Fax:  (607) 255-7149 Email:  alozano@math.cornell.edu Courses & Office Hours

Education

Ph.D. (2004) Boston University

Research Area: Number Theory

I study algebraic number theory, in particular p-adic Galois representations and their deformations, and connections with elliptic units and class number divisibility problems. I am also very interested in elliptic surfaces of high rank and constructing elliptic curves of high rank.

Selected Publications

Bernoulli numbers, Hurwitz numbers, p-adic L-functions and Kummer’s criterion, RACSAM (Journal of the Royal Academy of Science of Spain) 101 no. 1 (2007).

Constructing elliptic curves over Q(t) with moderate rank (with Scott Arms and Steven J.Miller), Journal of Number Theory 123 no. 2 (2007), 388–402.

On elliptic units and p-adic Galois representations attached to elliptic curves, Journal of Number Theory 117 no. 2 (2006), 29 pages.

On the surjectivity of Galois representations attached to elliptic curves over number fields, Acta Arithmetica 117 no. 3 (2005), 283–291.

On certain closed subgroups of SL(2,Z_p[[X]]), Revista Colombiana de Matemticas 39 (2005), 13–19.

Last modified: October 31, 2006