Introduction to Tropical Geometry

Abstract: We will give a gentle introduction to tropical geometry. We will begin with basic definitions of tropical algebra, tropical hypersurfaces and tropical varieties. We will then see the relationship with complex algebraic geometry via the approximation theorem. Time permitting we will speak about tropical homology and some tropical intersection theory. Then we will continue our introduction to tropical geometry by presenting some applications in real algebraic geometry, machine learning and Hodge conjecture.