This is an 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.
In this seminar we will study the foundations of Knot theory, which studies entanglements of closed curves in three dimensional space.
What seems like a simple subject in topology turns out to be a rich theory with applications to 3-manifolds, representation theory, physics and much more.