Perfect matchings in hypergraphs and the erdös matching conjecture

We prove a new upper bound for the minimum d-degree threshold for perfect matchings in k-uniform hypergraphs when d < k/2. As a consequence, this determines exact values of the threshold when 0.42k ≥ d < k/2 or when (k, d) = (12, 5) or (17, 7). Our approach is to give an upper bound on the Erdös matching conjecture and convert the result to the minimum d-degree setting using an approach of Kühn, Osthus, and Townsend. To obtain exact thresholds, we also apply a result of Treglown and Zhao.