Title: Graphs and combinatorics with a relationship to algebra, geometry and physicsSpeaker: Ralph Kaufmann Affiliation: Purdue Zoom: Contact Karen Yeats
Several algebraic and geometric structures are most naturally encoded via graphs. These include restrictions, such as trees, and decorations, such as planar graphs, ribbon graphs, bi-partite graphs (aka. hypergraphs), directed versions, etc. Particularly nice properties satisfy some kind of hereditary condition. This affords a dual perspective. Either as (nested) subsets and decomposition, or as composition, gluing locally. Both views relate to category theory, algebra, and combinatorics in terms of finite sets, cospans etc. We will give examples of these phenomena and provide a general background.
Title: The Erdos-Szekeres theoremSpeaker: Lukas Nabergall Affiliation: University of Waterloo Zoom: Contact Maxwell Levit
What lies at the intersection of combinatorial geometry, graph theory, order theory, analysis, and statistics? Why, only one of the most beautiful theorems you may have never heard of. Let me take you on a journey from early 20th century Budapest through to the heights of modern mathematics and show you why this classic result of Erdos and Szekeres is worth adding to your mathematical repertoire. Along the way we'll even see a proof so good it must come from The Book.