Abstract: We generalize an intersection-theoretic local inequality of Fulton-Lazarsfeld to weighted blowups. Using this together with the classification of 3-dimensional divisorial contractions, we prove nonrationality of many families of terminal Fano 3-folds. This is joint work with Igor Krylov and Takuzo Okada.
Abstract: Density dependence is a key ecological mechanism regulating population growth, yet its influence can vary substantially depending on which life stage it affects. Understanding these effects is critical for evaluating the success of Wolbachia-based mosquito population suppression strategies. We develop an ordinary differential equation model of Aedes aegypti dynamics that incorporates density-dependent regulation in development and mortality processes. Through analytical and numerical investigations, we show that when density dependence acts primarily on juvenile development, release-driven population suppression can produce counterintuitive, non-monotonic responses—where intermediate release rates transiently increase the uninfected adult population. In contrast, when density dependence acts only on juvenile mortality, this phenomenon does not occur. These findings highlight the importance of identifying which life-history processes are density-regulated when designing Wolbachia-based control programs.
Joint work with Alyssa Petroski (University of the Sciences), Lauren M. Childs (Virginia Tech), and Michael A. Robert (Virginia Tech).
Abstract: Surface Stokes equations have attracted significant recent attention in numerical analysis because approximation of their solutions poses significant obstacles not encountered in the Euclidean context. One of these challenges involves simultaneously enforcing tangentiality and continuity of discrete velocity approximations. Existing finite element methods all enforce one of these two constraints weakly either by penalization or by use of Lagrange multipliers. However, a robust and systematic construction of surface Stokes finite element spaces with nodal degrees of freedom is still missing. In this talk, we introduce a novel approach addressing these challenges by constructing surface finite element spaces with tangential velocity fields based on the classical Taylor-Hood pair. Functions in the discrete spaces are not continuous, but do have conormal-continuity, and the resulting methods do not require ad hoc penalization. We prove stability and optimal-order energy-norm convergence of the method and provide numerical examples illustrating the theory. At the end of the talk, we discuss analogous divergence-free pairs, based on the Scott-Vogelius element. This is joint work with Alan Demlow, Texas A&M.