2016
Many physical systems admit mathematical models from contact geometry, and symmetries of the corresponding geometric structure provide the modeler with insights that can be obtained in no other way. In this talk I will introduce contact geometry through a selection of examples arising from fluid mechanics, Hamiltonian dynamics, and Riemannian geometry. Finally because contact geometry is defined using the language of differential forms, it may seem appropriate for only those problems that admit smooth formulations; however if time permits I will also explain the extension of smooth contact dynamics to topological dynamics.
As events of the past decade have tragically demonstrated, tsunamis pose a major risk to coastal populations around the world. Numerical modeling is an important tool in better understanding past tsunamis and their geophysical sources, in real-time warning and evacuation, and in assessing hazards and mitigating the risk of future tsunamis. I will discuss a variety of techniques from adaptive mesh refinement to probabilistic hazard analysis that are being used for tsunamis and related geophysical hazards.
2015
Computer-assisted or automated analysis of atomic-scale resolution image for polycrystalline materials has important applications in characterizing and understanding material micro-structure. In this talk, we will discuss some recent progress in crystal image analysis using 2D synchrosqueezed transforms combined with variational approaches. This talk is based on joint works with Benedikt Wirth, Haizhao Yang and Lexing Ying.