This talk reports on our recent development of high-resolution, nonionizing biophotonic imaging technologies, including optical coherence tomography (OCT) and multiphoton endomicros- copy. These fiber-optically based technologies have shown significant translational potential for imaging tissue microanatomiesin vivoat a resolution approaching or at that of standard histopathology but without the need for tissue removal or staining. The physics principles, engineering challenges and (big) data and image processing challenges, and potential solutions will be briefly discussed, including the development of advanced lasers, MEMS technology, custom optical fiber, ultracompact and high-performance micro optics, speckle noise reduction, image segmentation and optical staining techniques. Representative applications of these high-resolution technologies will be presented,

In the first lecture, I will discuss an extension of the Alperin weight conjecture to permutation modules M of a finite group. By introducing relative projectivity and the theory of vertices and sources, we may partition the set of primitive idempotents of End(M) in terms of their defect groups. In this way, we may provide a classification of simple modules of End(M).

In this talk, I will report our recent research on a reaction-advection- diffusion competition model in a periodic habitat. We first investigate the global attractivity of a semi-trivial steady state (i.e., the competitive exclusion) for the periodic initial value problem. Then we establish the existence of the rightward spreading speed and its coincidence with the minimal wave speed for spatially periodic rightward traveling waves. Further, we obtain a set of sufficient conditions for the rightward spreading speed to be linearly determinate. Finally, we apply the obtained results to a prototypical reaction-diffusion model. This is a joint work with Dr. Xiaoqiang Zhao.

I will talk about the application of algebraic and number theoretical methods in the study of two combinatorial structures: difference sets in design theory and Cameron-Libler line class in finite geometry. The first concerns the multiplier conjecture, while the other has its origin in the study of permutation groups. What they have in common is that results from algebraic number theory plays important role in the proof. The second part is a joint work with Koji Momihara and Qing Xiang.

In this talk, I will establish a defect relation for holomorphic curves intersecting general divisors in projective varieties. Various consequences will be discussed.

学术报告题目: Preserver problems报告人: 李志光(Chi-Kwong Li)教授, 美国威廉玛丽学院摘要: Preserver problems concern the study of the characterizations of transformations on matrices or operators having some special properties such as leaving invariant certain functions, subsets, or relations. The study has motivations from theoretical and applied problems. We will give an introduction of the to...

学术报告报告人：刘跃教授(University of Texas at Arlington)题目： On the rotation- two- component- Camassa-Holm system modelling the equatorial water waves时间：2015年6月17日(星期三)下午10：00—11：00地点：数学系致远楼102欢迎各位参加

学术报告报告人：张平正教授(江苏大学)题目： The Holder continuity of the solution map to the Camassa - Holm equation in weak topology时间：2015年6月17日(星期三)上午10:30—11：30地点：数学系致远楼102欢迎各位参加