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R. Amzi Jeffs, Intersection patterns of convex sets
Wednesday, August 9, 2023 @ 4:30 PM - 5:30 PM KST
How can one arrange a collection of convex sets in d-dimensional Euclidean space? This guiding question is fundamental in discrete geometry, and can be made concrete in a variety of ways, for example the study of hyperplane arrangements, embeddability of simplicial complexes, Helly-type theorems, and more. This talk will focus on the classical topic of d-representable complexes and its more recent generalization to convex codes. We will show how these frameworks differ, share some novel Helly-type results, and offer several tantalizing open questions.