Title: On a new partitioning problem

Abstract: I will first review the classical partitioning problem, discuss the double/triple/K-bubble conjectures, and introduce a new partitioning problem that arises in the study of triblock copolymers in certain limiting regimes. I will present the setting for this new geometrical problem, discuss existence and uniqueness of locally minimizing solutions as well as answers to several conjectures. These represent joint works with Stan Alama, Silas Vriend, Mike Novack, Robin Neumayer and Anna Skorobogatova.