Use the library’s online research guides and exhibits about Mexico to play Jeopardy and win a $20 Starbucks card.  http://libguides.uky.edu/vivamexico/iew

Usa las guías digitales sobre las exhibicnes de México para jugar Jeopardy Mexicano y tener una oportunidad de ganas $20 hacia Starbucks,  http://libguides.uky.edu/vivamexico/iew

Title:  Some progresses on two-dimensional Riemann problems in gas dynamics

Abstract:  Two dimensional Riemann problems for compressible fluid flows assume the simplest piecewise sectorial initial state but provide the most fundamental wave configurations, including the reflection of oblique shocks and vortex-shock interaction etc. In this talk I will show many fascinating pictures, based on 2D Riemann solutions, to disclose the mysteries of compressible fluid world both through analytical tools (in the form of mathematical theorems) and computational techniques (in the form of simulations). The analysis is based on the characteristic decomposition theory we developed recently, while the simulations are obtained using the generalized Riemann problem (GRP) scheme that is equipped with a highly accurate solver in the construction of numerical fluxes by a way of tracking singularities analytically and keeping entropy exactly computed. 

Title:  Smoothness of isometries between subRiemannian manifolds

Abstract:  In a joint work with Enrico Le Donne (Jyvaskyla, Finland), we show that the group of isometries (i.e., distance-preserving homeomorphisms) of an equiregular subRiemannian manifold is a finite-dimensional Lie group of smooth transformations. The proof is based on a new PDE argument, in the spirit of harmonic coordinates, establishing that in an arbitrary subRiemannian manifold there exists an open dense subset where all isometries are smooth.

Title:  Higher-order analogues of the exterior derivative complex

Abstract:  I will discuss some earlier joint work with E. M. Stein concerning div-curl type inequalities for the exterior derivative operator and its adjoint in Euclidean space R^n. I will then present various higher-order generalizations of the notion of exterior derivative, and discuss some recent div-curl type estimates for such operators. Part of this work is joint with A. Raich.

Under the leadership of Prime Minister Abe, the Japanese government is proactively working to solve the major challenges Japan faces. Consul-General Kato discusses these challenges and outlines Japan’s path for-ward to prosperity.