Sabrina Pauli (TU Darmstadt) - BKK Theorem: Tropical and Arithmetic Perspectives

The Bernstein–Khovanskii–Kushnirenko (BKK) theorem gives a way to count the non-zero solutions of a system of polynomial equations using geometric objects called Newton polytopes. It can be seen as a refinement of Bézout’s theorem. One particularly nice proof of this result uses ideas from tropical geometry, where complicated algebraic problems can be translated into simpler, combinatorial ones. In this talk, I will explain the BKK theorem and sketch its proof using tropical geometry. I will also describe joint work with Andrés Jaramillo Puentes, where we extend this result to more general base fields, not just algebraically closed ones. This leads to a meaningful way to count solutions in a broader setting, again using tropical methods.