Combinatorics: Rom Pinchasi (Technion)

Date: 
Mon, 27/01/202512:00-14:00
Location: 
Ross 63
title: Digons in arrangements of pairwise intersecting pseudocircles - Proof of Gr\"unbaum's Conjecture
Abstract: A conjecture of Branko Grünbaum from 1972 states that any simple arrangement of $n$ pairwise intersecting pseudocircles in the plane can have at most $2n-2$ digons. In the first part of the talk we will present our full solution of Gr\"unbaum's Conjecture for arrangements of pairwise intersecting geometric circles. In the second part of the talk we will present our solution of Gr\"unbaum's Conjecture in full generality. The general solution is independent of the solution for the case of circles, but it uses an abstract idea from the first part of the talk, without which the proof of the general case of Gr\"unbaum's Conjecture could not be carried out.
This is a joint work with Eyal Ackerman, Gabor Damasdi, Balazs Keszegh, and Rebeka Raffay