Liza Ter-Saakov — Matroids and the Lattice of Flats
Matroids are a very interesting object in combinatorics/algebra that have been rising in popularity as something to study in the past decade, including in work whose authors have received Field Medals. They can be defined in many equivalent ways (cryptomorphisms), and this talk introduces a couple of them. We will focus on the flat definition of a matroid, and explore the lattice that one obtains from the flats. We'll introduce basic lattice theory then investigate what we can say about matroids from their lattices and what we can say about lattices from their matroids.
Some questions one could ask: Can we characterize the lattices that come from flats of matroids? (yes!) Can we predict how changing a matroid changes the lattice of flats? (depends on the change!) Does augmenting the lattice by [insert way here] give us another matroid, and if so, are there relations between the new and old matroid? (sometimes!) Do lattices of matroid flats have any special properties? (yes, some of which are topology related!) There are a plethora of exciting questions to ask and this talk seeks to pose many, and answer most.
Estimathon
This is a team-based contest that combines trivia, game theory, and mathematical thinking. Teams have 30 minutes to work on a set of 13 estimation problems, the winning team being the one with the best set of estimates. Come join us for a fun time and food!
