Mathematics 790STF - IntroTropicalGeometry&Combinat

Tropical geometry studies algebraic varieties through their images under the tropical semiring, replacing addition with minimum/maximum and multiplication with addition. This course develops the foundations and central tools of the subject and shows how tropical methods encode rich algebro-geometric, combinatorial, and polyhedral information. Core themes include tropical varieties and their fans, initial degenerations, Grobner and Newton polyhedra, intersection theory, and connections to moduli, matroids, and enumerative geometry, explored via concrete and computational examples. If time permits, recent developments such as Baker?Bowler theory, hyperstructures, and connections to Lorentzian polynomials will be discussed.

MATH 611 & 612