Seminar Details
2026-03-31 (14:00) : Envy-free divisions of cakes: recent results and open questions
At Euler building (room A.002)
Organized by Mathematical Engineering
Speaker :
Frédéric MEUNIER (Paris-tech )
Abstract :
The envy-free cake-cutting problem asks for a way to divide a cake (identified with the interval [0,1]) among players with different tastes so that each receives a connected piece and no one envies another’s share. The Stromquist–Woodall theorem from 1980 guarantees the existence of such an envy-free division under mild assumptions. Recently, there has been a surge of interest in this problem from various perspectives — computer science, social choice theory, economics, and topological combinatorics. In this talk, we present several extensions, from these perspectives: the cake may be “poisoned,” there may be multiple cakes with joint preferences, or the cake may be discrete (as in the necklace-splitting problem). We will also discuss several challenging open questions. This talk is based on joint work with Ayumi Igarashi, Francis Su, and Shira Zerbib.