Abstract: The topology of a manifold determines if a flow has fixed points, as stated in the Poincaré-Hopf theorem, but if a manifold (oriented) admits a flow without fixed points it also admits a flow without periodic orbits. If the manifold has dimension 2, this assertion is almost trivial. In... read more
Abstract: Matroids are a mathematical structure that generalize the linear independence in vector spaces and acyclic subgraphs in graphs, and have been applied in combinatorial optimization and discrete math. In the matroid secretary problem, a matroid M is given and an adversary assigns a... read more
Abstract: We develop a boundary integral method for computing the forces on a spherical particle in an unsteady viscoelastic flow. We establish a boundary integral equation (BIE) in the Fourier domain using a correspondence principle between Stokes flow and linear ... read more
Applied mathematicians develop and utilize mathematically rigorous methods, modeling insights, and computational algorithms to solve real-world problems. Applied mathematics is the mathematics that is created in response to problems in science, engineering, and society.