# Number Theory and Arithmetic Geometry

**Problems about distribution of prime numbers**. Study of the distribution of prime numbers and other numbers satisfying specific arithmetic properties. Additive problems with prime numbers, distribution of arithmetic functions and study of exceptional sets of the most known conjectures of the number theory.**Linear recurrences.**Study of the arithmetic properties of terms of linear recurrences of integers and other classical sequences of integers, with a special focus on prime factors and divisibility properties.**Continued fractions and generalizations.**Study of approximations and periodic representations of algebraic irrationalities by means of continued fractions and their generalizations.**Diophantine geometry:**problems of unlikely intersections in families of abelian varieties, integral points on algebraic varieties over number fields and function fields, solvability of diophantine equations in integers and polynomials.