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Rainie Heck: Vector sum problems in convex and discrete geometry

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Tuesday, 28. October 2025, 12:30 - 13:30
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.

We inform you that this talk is also the internal defense of Rainie Heck's PhD dissertation.

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