Vector-Valued Polynomial Equations, Toric Vector Bundles and Matroids

This lecture explores vector-valued polynomial equations, toric vector bundles, and matroids as part of the "Combinatorial Synergies in Geometry and Number Theory" workshop organized by the Instituto de Matemática Pura e Aplicada. Delivered by Kiumars Kaveh from Pittsburgh, USA, the talk delves into the intersection of combinatorial methods with algebraic geometry and number theory. The workshop features mini-courses and presentations by international mathematicians focusing on enhancing combinatorial approaches to geometric and arithmetic structures, bringing together both early-career researchers and specialists in the field. Explore how combinatorial methods are embedded in various areas of mathematics through this theoretical presentation that contributes to the broader discussion of synergies between combinatorics and other mathematical disciplines.