Georgia Institute of Technology College of Sciences

Further discussion of alternative metrics on RNA secondary structures.

Metric graphs arise naturally in tropical tropical geometry and Berkovich geometry. Recent efforts have extend conventional notion of divisors and linear systems on algebraic curves to finite graphs and metric graphs (tropical curves). Reduced divisors are introduced as an essential tool in proving graph-theoretic Riemann-Roch. In short, a q-reduced divisor is the unique divisor in a linear system with respect to a point q in the graph. In this talk, I will show how tropical convexity is related to linear systems on metric graphs, and define a canonical metric on the linear systems. In addition, I will introduce a generalized notion of reduced divisors, which are defined with respect to any effective divisor as in comparison a single point (effective divisor of degree one) in the conventional case.

In fluid dynamics, one of the most classical issues is to understand the dynamics of viscous fluid flows past solid bodies (e.g., aircrafts, ships, etc...), especially in the regime of very high Reynolds numbers (or small viscosity). Boundary layers are typically formed in a thin layer near the boundary. In this talk, I shall present various ill-posedness results on the classical Prandtl equation, and discuss the relevance of boundary-layer expansions and the vanishing viscosity limit problem of the Navier-Stokes equations. I will also discuss viscosity effects in destabilizing stable inviscid flows.