Department of

August 2020September 2020October 2020 Su Mo Tu We Th Fr Sa Su MoTuWe Th Fr Sa Su Mo Tu We Th Fr Sa 1 1 2 3 4 5 1 2 3 2 3 4 5 6 7 8 6 7 8 9 10 11 12 4 5 6 7 8 9 10 9 10 11 12 13 14 15 13 14 15 16 17 18 19 11 12 13 14 15 16 17 16 17 18 19 20 21 22 20 21 22 23 24 25 26 18 19 20 21 22 23 24 23 24 25 26 27 28 29 27 282930 25 26 27 28 29 30 31 30 31

Thursday, September 10, 2020

**Abstract:** A substantial number of results and conjectures deal with the existence of a set of prescribed type which contains a fair share from each member of a finite collection of objects in a space. Examples include the Ham-Sandwich Theorem in Measure Theory, the Hobby-Rice Theorem in Approximation Theory, the Necklace Theorem and the Ryser Conjecture in Discrete Mathematics, and more. The techniques in the study of these results combine combinatorial, topological, geometric and algebraic tools. I will describe the topic, focusing on several recent results.