Colloquium: Tuesday, January 1, 2019. Speaker: Karim Adiprasito (Hebrew University). Title: “From Hall’s marriage theorem to algebraic geometry (and back to combinatorics)”.
We discuss how something remarkably similar to Hall’s marriage theorem appears naturally in context of a conjecture of Grothendieck in algebraic geometry, and how this is useful to prove some long-standing problems in discrete geometry. For instance, I will prove that for a simplicial complex Δ that embeds into R^(2d), the number of d-dimensional simplices exceeds the number of (d−1)-dimensional simplices by a factor of at most d+2. This generalizes a result going back to Descartes and Euler, and resolves the Grünbaum-Kalai-Sarkaria conjecture.
Tea will be served before the talk (at 13:50).
