Large substructures in hypergraphs

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An important question in modern graph theory is whether a given graph contains certain large substructures such as perfect matchings or Hamilton cycles. This project seeks to advance our understanding of these problems in the setting of hypergraphs. The proposed research considers a series of open questions concerning minimum degree conditions and Ramsey numbers of tight cycles, paths and trees in hypergraphs. To solve these problems, new techniques based on hypergraph regularity and the absorption method will be developed, which could be of independent interest.