学术报告报告题目1：DefectCurves in a Modified Ericksen Model of Nematic Liquid Crystals
报告人：ProfessorRobert Hardt(美国莱斯大学)
报告时间：2016年6月21日（星期二）上午09:30-10:30
报告题目2：BoundaryBlow-up analysis for 2 dimensional approximate harmonic maps undereither weak or strong anchoring boundary conditions.
报告人：王长友 教授(美国普渡大学)
报告时间：2016年6月21日（星期二）上午10:30-11:30
报告地点：4号楼4318室
欢迎广大师生前往！
数学学院
2016年06月20日
报告1摘要：
In 1985, J. Ericksen derived a model for uniaxial liquid crystals toallow for disclinations (i.e. line defects or curve singularities).It involved not only a unit director vectorfield on a region of R^3but also a scalar order parameter quantifying the expected innerproduct between this vector and the molecular orientation. FH.Lin, inseveral papers, related this model, for certain material constants,to harmonic maps to a metric cone over S^2 . He showed that aminimizer would be continuous everywhere but would have higherregularity fail on the singular defect set of points mapped to thecone point. The optimal partial regularity result ofR.Hardt-FH.Lin in 1993, for this model, improved this to regularityaway from isolated points. This result unfortunately still excludedline singularities. This paper accordingly also introduced a modifiedmodel involving maps to a metric cone over RP^2, the real projectiveplane. Here the nontrivial homotopy leads to the optimal estimate ofthe singular set being 1 dimensional. In 2010, J. Ball and A.Zarnescudiscussed a derivation from the de Gennes Q tensor and interestingorientability questions involving RP^2 . In recent work with FH.Linand O. Alper, we see that the singular set with this RP^2 cone modelnecessarily consists of Holder continuous curves.
报告2摘要：
In this talk, I will describe the boundary bubbling phenomena forapproximate harmonic maps in dimension two under either weak orstrong anchoring boundary conditions, which concludes that, amongother properties, the total energy is conserved after counting theenergy of bubbles. This is a joint work with Tao Huang.