This is a standard introductory course to the theory of curves and surfaces
Algebraic geometry is the common language for many branches of modern research in mathematics. This course gives an introduction to this field by studying algebraic curves and their intersection theory.
P-adic numbers are a number theoretic analogue of the real numbers, which interpolate between arithmetics, analysis and geometry. In this course we study their basic properties and give various applications, notably we will prove rationality of the Weil Zeta function.
This course presents geometric constructions of irreducible representations of semi-simple Lie Algebras and their Weyl groups by means of Springer theory.