In this talk I will first introduce the motivation and basic constructions of the Dubrovin-Zhang theory, with emphasis on the axiomatic description of the Dubrovin-Zhang hierarchy. Then I will explain the Dubrovin-Zhang polynomiality conjecture, which is a long-standing and important conjecture. I will briefly introduce our proof to this conjecture. Finally I will address important open problems, mainly concerning with the relations with Buryak's double ramification hierarchies. The talk is based on the joint work with Si-Qi Liu and Youjin Zhang.

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