기초과학연구원 이산수학그룹
On July 2, 2024, Kisun Lee (이기선) from Clemson University gave a talk at the Discrete Math Seminar on a combinatorial characterization of symmetric matrices of symmetric tropical rank 2. The title of his talk was “symmetric tropical rank 2 matrices“.
Tropical geometry replaces usual addition and multiplication with tropical addition (the min) and tropical multiplication (the sum), which offers a polyhedral interpretation of algebraic variety. This talk aims to pitch the usefulness of tropical geometry in understanding classical algebraic geometry. As an example, we introduce the tropicalization of the variety of symmetric rank 2 matrices. We discuss that this tropicalization has a simplicial complex structure as the space of symmetric bicolored trees. As a result, we show that this space is shellable and delve into its matroidal structure. It is based on the joint work with May Cai and Josephine Yu.