美国佛罗里达州立大学Craig A. Nolder教授讲学通知

 

受学校国际合作与交流基金资助，应理学院数学系包革军教授邀请，美国佛罗里达州立大学数学系Craig A.Nolder教授将于5月9日--5月17我校访问讲学并进行学术交流，现将讲学时间、地点、内容通知如下，欢迎相关专业老师和同学参加。

 

时间：5月10日 14:00

地点：正心楼 528

摘要：The complex numbers are the basis of complex analysis. They are the Clifford algebra associated with the quadratic space which consists of the Euclidean plane with quadratic form . The compactification of this plane is the Riemann sphere, which topologically is the one point compactification of the plane. The theory of Mobius transformations and rational functions naturally exists on this sphere. This includes fixed points, transitivity and the degree of a mapping in particular. The theory here is classical. The Euclidean plane with the quadratic form  has the split complex numbers as its associated Clifford algebra. The compactification in this case in a projectivized torus in . This lecture will describe the geometry of this compactification. This is relatively new theory and is related to physics, in particular special relativity.

 

时间：5月13日 14:00

地点：正心楼 528

摘要： We will describe the Mobius theory and discuss the fixed points of these transformations and transitivity. We also address the degree of rational mappings. A technical difficulty here is the lack of a fundamental theorem of algebra.

 

时间：5月14日 14:00

地点：正心楼

摘要：Analytic functions in the plane are conformal at nonsingular points. This means that they locally map circles to circles. Quasiconformal mappings are an important generalization of conformality as they locally map circles to ellipses of bounded distortions. We have recently discovered that Clifford analytic functions in space are quasiconformal at nonsingular points. Moreover in many cases, the quasiconformality is global over certain.

 

时间：5月16日 14:00

地点：正心楼 528

 摘要：We will discuss particular examples. These include the Cauchy kernel and generalizations which are so called p-monogenic. Solutions to the Euclidean Dirac operator are called monogenic of Clifford analytic. The p-monogenic functions are solutions to similar nonlinear Dirac operators. We also discuss the quasiconformality of quadratic monogenic functions and consider extensions to higher degree monogenic functions in space

 

时间：5月17日 14:00

地点：正心楼 528

摘要：The processing of oceanic and atmospheric data is important to the understanding of the behavior of ocean currents and the interaction with the atmosphere. This involves particular extreme events such as tsunamis and exceptional weather. The Hilbert transform is used in one dimension to give a dynamic view of the processed data in the phase space. Current research is now considering the use of higher dimensional Hilbert transforms to process higher dimensional data in a similar way. These transforms are based on Clifford analysis in these dimensions. We propose to describe this and our current research in there areas.