turkmath.org

The group $SL(2,Z)$ of 2 by 2 matrices with integral entries and determinant 1 occurs in many contexts in mathematics. In this talk we study this group for its own sake. Despite the fact that it is neither finite nor a Lie group it is full of interesting structures. We shall see how questions concerning properties of its subgroups lead to beautiful and stimulating discrete structures, how questions concerning its finite dimensional representations lead to interesting partly still unsolved problems, and we shall see how tightly it is connected to the heart of number theory, the theory of algebraic equations with algebraic coefficients.