Baruch Discrete Math Group

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Given a geometric object, the problem of dividing it fairly among several guests is an interesting problem. Depending on the rules to make a partition and our definition of fairness, sometimes it is possible and sometimes it is not. Surprisingly, many sharp results on this area are proved using tools of algebraic topology. In this talk we will discuss recent advances related to measure partitions and how, as one modifies the problem, we need to change the underlying topological tool behind the proof. We will also introduce new results on envy-free distribution of resources.