# Paloma Bengoechea

# About me

I am currently an Ambizione fellow at ETH Zürich. My Ambizione project focuses in the interactions between the fields of Modular Forms and Diophantine Approximation. I also work on the conjecture of Maeda on the irreducibility of Hecke polynomials and the maximality of their Galois group.

In the period 2013-2016 I was a postdoctoral researcher at the University of York with Sanju Velani and Victor Beresnevich in the EPSRC Programme Grant New Frameworks in Metric Number Theory. During that time I worked on different problems in Diophantine approximation, such as studying sets of badly approximable numbers and their Hausdorff dimension, or the p-adic Littlewood Conjecture. Among the techniques involved in my work are the construction of Cantor sets with maximal Hausdorff dimension and Schmidt games.

In July 2013 I defended my PhD thesis Corps quadratiques et formes modulaires supervised by Don Zagier at Universite Pierre et Marie Curie (Paris 6). My PhD addresses different problems in the theory of modular forms and their interrelations with the reduction of binary quadratic forms, continued fractions, and the theory of complex multiplication.