Recorded 14 February 2025. Felipe Rincon of Queen Mary University of London presents "Tropical Ideals" at IPAM's Computational Interactions between Algebra, Combinatorics, and Discrete Geometry Workshop. Abstract: Tropical ideals are combinatorial objects that abstract the behavior of the collections of subsets of lattice points that arise as the supports of all polynomials in an ideal. Their structure is governed by a sequence of ‘compatible’ matroids and, even though most tropical ideals are not realizable by an ideal of polynomials, they share many properties with usual ideals in a polynomial ring. In this talk, I will introduce the notion of tropical ideals and discuss various works studying some of their properties and their possible associated (tropical) varieties. I will also share results about the class of matroids that can be represented as the variety of a tropical ideal and highlight some computational challenges. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/computational-interactions-between-algebra-combinatorics-and-discrete-geometry/