Fair division of bundles
Abstract: There are a few purely combinatorial problems that can be solved with topological methods. In this talk, we will discuss a new fair division problem for which tools from topology can be used to obtain a solution. The goal is, given a set of bundles (packages) with different valuations, to distribute them fairly among several participants. This could be done by breaking some bundles apart and distributing the contents. We seek fair distributions that maximize the number of full bundles each participant receives. The tools used for this problem use a configuration space constructed by Vucic and Zivaljevic to count the number of Tverberg partitions for finite sets of points in R^d.
Event Type: Seminar. Research Area: Discrete Math and Combinatorics. Location: MSC E406. Speaker Name: Pablo Soberon. Speaker Institution: CUNY.
Friday, May 1, 2026, 2:00 PM – 3:00 PM.
A discrete view of Gromov's filling area conjecture
Abstract: In differential geometry, a metric surface $M$ is said to be an isometric filling of a closed metric curve $C$ if $\partial M=C$ and $d_M(x,y)=d_C(x,y)$ for all $x,y\in C$. That is, $M$ does not introduce any ``shortcuts'' between points on its boundary. Gromov’s filling area conjecture from 1983 asserts that among all isometric fillings of the Riemannian circle, the one with the smallest surface area is the hemisphere. Gromov’s conjecture has been verified if, say, $M$ is homeomorphic to the disk and in a few other cases, but it is still open in general. Admittedly, I’m not a differential geometer, so we consider instead a particular discrete version of Gromov’s conjecture which is likely fairly natural to anyone who studies graph embeddings on arbitrary surfaces. We obtain reasonable asymptotic bounds on this discrete variant by applying standard graph theoretic results, such as Menger’s theorem. These bounds can then be translated to the continuous setting to show that any isometric filling of th…
Event Type: Seminar. Research Area: Discrete Math and Combinatorics. Location: MSC E406. Speaker Name: Chris Wells. Speaker Institution: Auburn University.
Thursday, May 14, 2026, 11:00 AM – 12:00 PM.