Teaching assistant at University of Barcelona (1986-90).
At the Polytechinc Universtity of Catalonia since 1990.
Currently Associate Professor at the Mathematics Department.
Member of the Barcelona Number Theory Seminar (STNB).
PhD Advisor of Ramiro Moreno’s thesis “Sylow subgroups of elliptic curves defined over finite fields”
- Algebraic Number Theory
- Galois representations
- Elliptic and hyperelliptic curves in Cryptography
- Hopf Galois theory.
- Octahedral Galois representations arising from Q-curves of degree 2. Julio Fernández, Joan-Carles Lario, Anna Rio. Canadian Journal of Mathematics 54 (2002) 1202-1228
- Dyadic exercises for octahedral extensions II. Anna Rio. Journal of Number Theory 118 Num. 2 (2006) 172-188
- Computing the l-power torsion of an elliptic curve over a finite field. Josep M. Miret, Ramiro Moreno, Anna Rio, Magda Valls. Mathematics of Computation, 78 Num. 267(2009), 1767-1786
- Halving for the 2-Sylow subgroup of genus 2 curves over binary fields. Josep M. Miret, R. Moreno, Jordi Pujolàs, Anna Rio. Finite Fields and Their Applications 15 Num. 5 (2009) 569-579
- Non isomorphic Hopf Galois structures with isomorphic underlying Hopf algebras. Teresa Crespo, Anna Rio, Montserrat Vela. Journal of Algebra, Volume 422 (2015) 270-276