Xiaodong Yan
Biography: Xiaodong Yan is a professor at the University of Connecticut. Her research is nonlinear partial differential equations with a focus on regularity issues in elliptic/parabolic systems and pattern formations. Her recent research focuses on nonlinear PDEs from materials science
Title: PDEs from materials science
Abstract: Materials science has been a rich source for PDE models. Many questions from solid-solid phase transitions in nonlinear elasticity, thin films and crystals can be formulated as a variational problem involving non-convex integrals and small parameters coming from approximation process or discretization arguments. The minimizers or stationary points of which correspond to the experimentally observed materials structure. In this talk, I will introduce some PDE problems originated from thin films and smectic liquid crystals and briefly explain recent progress on the analysis of those problems.
Lisa Naples
Biography: Lisa Naples is an Assistant Professor at Fairfield University. Her research interests lie in geometry of measures and metric analysis. She earned her Ph.D. at the University of Connecticut before spending time as a visiting faculty member at Macalester College.
Title: Size and Structure
Abstract: Given a set, a basic question that one may ask is: “What is the size of the set?” The way that we answer this question may be dependent on the structure of the set. For example, if the set is a line or curve segment, we will likely calculate the length. On the other hand, if the set is a polygonal region, we will calculate the area. Of course, the structure of sets that we encounter in Euclidean space may be much more diverse than curves or polygons. In this talk we will follow a line of questioning to build up relationships between size and structure that persist even when the sets are of less familiar shape. Along the way, we will highlight some important concepts from calculus and real analysis that help us to answer our existing questions as well as develop new ones.