Tropical Ideals and Their Properties in Computational Algebra

Explore a 54-minute lecture from Queen Mary University of London's Felipe Rincon at IPAM's Computational Interactions between Algebra, Combinatorics, and Discrete Geometry Workshop, delving into the fascinating world of tropical ideals. Discover how these combinatorial objects abstract the behavior of lattice point subset collections arising from polynomial ideal supports. Learn about the governing structure of compatible matroids and understand why, despite most tropical ideals not being realizable by polynomial ideals, they maintain similar properties to usual polynomial ring ideals. Examine the concept of tropical ideals, their properties, and associated varieties while investigating which matroids can be represented as tropical ideal varieties. Gain insights into computational challenges in this field and understand the intersection of algebra, combinatorics, and discrete geometry in modern mathematical research.