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The study of completely positive maps is motivated by applications of the theory of completely positive maps to quantum information theory, where operator valued completely positive maps on C*-algebras are used as a model for quantum operation, and quantum probability. Stinespring theorem is a very famous representation theorem in C*-algebras. In this talk, we give an analogue of stinespring theorem in Hilbert A-module. And we also consider the covariant representation on Hilbert C*-module.

报告人：香港理工大学数学系祁力群教授.报告题目：A Necessary and Sufficient Condition for Existence of a Positive Perron Vector时间: 2015年12月8日(周二)下午16:00.地点: 数学系107室.欢迎大家前往听讲

We give a brief overview on the current investigations in this area. We concentrate on the three themes: 1.Integral representations of nonlinear orthogonally additive operators; 2.Narrow orthogonally additive operators; 3.Extensions of orthogonally additive operators.

In this talk, I will give a geometric construction of the quantized enveloping algebras of type ADE and their bases via cyclic quiver varieties. The construction respects BGP reflections, which turns out to be Lusztig’s symmetries acting on these algebras.

题目： Vertex coloring and induced odd cycles of graphs报告人： 许宝刚教授（南京师范大学）时间： 12月4日周五下午 4:00-5:00pm地点： 宁静楼104欢迎各位参

The past decade has witnessed great progress in the development of nonlinear cointegrating regression. Unlike linear cointegration and nonlinear regression with stationarity where the traditional and classical methods are widely used in practice, estimation and inference theory in nonlinear cointegrating regression produce new mechanisms involving local time, a mixture of normal distributions and stochastic integrals. This talk aims to introduce the machinery of the theoretical developments in nonlinear cointegrating regression, providing up-to-date results on convergence to local time, extended martingale limit theorems and weak convergence to stochastic integrals for econometric applications.

In this paper, we find a novel approach to determine the number of common driving Brownian motions latent in the high dimensional Ito process using high frequency data. The high dimensional Ito process is first approximated locally on a shrinking block by discrete-time approximate factor model. We then estimate the number of common driving Brownian motions by minimizing the penalized aggregated mean-squared residual error. It turns out the estimated number is consistent to the true number. While the local mean-squared residual error on each block converges at the rate of $n^{1/4} /wedge /sqrt{p} $ where $n$ is the sample size and $p$ is the dimensionality, it is interesting that the aggregated mean-squared residual error converges at a higher rate of $/sqrt{n}/wedge p$.

In this talk, we will investigate the dynamics of delay differential equations which arise from modeling the transmission of avian influenza among migratory birds. We use dimension reduction method and asymptotic techniques to approximate the dynamic thresholds of avian influenzas models. This talk is based on a joint work with Jianhong Wu of York University.