Time: October 28, 2025 12:30 pm

Location: Riesz lecture hall, Bolyai Building, Aradi vértanúk tere 1., Szeged, Hungary

Abstract: In this talk we will focus on two problems from discrete and convex geometry: the vector balancing problem and the Steinitz problem. After introducing each problem and its history (including a surprising connection between them!), we present results for a generalization of vector balancing and for a reduction of the Steinitz problem. More precisely, we study a geometric generalization of the vector balancing problem called colorful vector balancing, and we show that two important results from the original problem also hold (and are tight and asymptoticaly tight, respectively) in the colorful setting as well. We also prove a reduction of the Steinitz problem to a more approachable setting, offering a potential proof avenue for a long standing open conjecture.