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ABSTRACT: The present talk is devoted to introducing estimates for the half-time derivative in the context of parabolic partial differential equations. We then discuss applications of these estimates to the following problems: (1) the parabolic conormal problem with leading coefficients that are merely measurable in time on Reifenberg-flat domain; (2) the L2-theory for poroelastic equations; (3) the path regularity of stochastic partial differential equations(SPDEs).