重庆大学数学中心学术活动：重庆分析研讨会
时间：2011年8月27日星期六
地点：重庆市沙坪坝区重庆大学A区主教504
主办：西南大学，重庆工商大学，重庆大学联合主办
联系人：马攀（15310277115）,王子鹏（13667643057）
请要参与的同学或老师在8月21日之前，发邮件到zipengwang20071@163.com.
具体报告安排
9:20 开始
9:30-10:20 李寒峰 (SUNY at Buffalo, USA)
Algebraic dynamical systems and operator algebras
10:20-10:50 茶歇
10:50-11:40 郭坤宇 (复旦大学,国家杰出青年基金获得者,长江教授 )
Multiplication operators on the Bergman space
8月27日下午
2:00-2:50 吕克宁 (Brigham Young University, USA ,千人计划获得者,四川大学 )
Lyapunov Exponents, Entropy, and Chaos for Random Dynamical Systems in a Banach Space
2:50-3:30 茶歇
3:30-4:20 Pierre Magal (University of Bordeaux, France)
Bifurcation Problems for Structured Population Dynamics Models
4:30-5:20许全华（Université de Franche-Comté, France,千人计划获得者,武汉大学）
Harmonic analysis on quantum tori
重庆分析研讨会
报告摘要：
Algebraic dynamical systems and operator algebras
李寒峰 (SUNY at Buffalo, USA)
An algebraic action is an action of a countable group on a compact metrizable abelian group by continuous automorphisms.Much was
known about the algebraic actions of finitely generated free abelian groups, for which commutative algebra is the main tool. I will review recent
progress towards understanding the algebraic actions of nonabelian groups, for which operator algebras play a vital role.
Multiplication operators on the Bergman space
--the connection between operator theory and von Neumann algebras
郭坤宇 (复旦大学)
In this talk, we will combine methods of complex analysis, operator theory and conformal geometry to attack some basic problem in the
theory of von Neumann algebras. The talk will exhibit fascinating connections between complex analysis, operator theory, von Neumann
algebras, geometry and group theory (jointly with Hanson Huang).
Lyapunov Exponents, Entropy, and Chaos for Random Dynamical Systems in a Banach Space
吕克宁 (Brigham Young University, USA and四川大学 )
We study the Lyapunov exponents and their associated invariant subspaces for infinite dimensional random dynamical systems in a
Banach space, which are generated by, for example, stochastic or random partial differential equations. We prove a multiplicative ergodic
theorem. We also prove that for an infinite dimensional random dynamical system with a random invariant set such as random attractor, if it’s
topological entropy is positive, then the dynamics on the random invariant set is chaotic.
Bifurcation Problems for Structured Population Dynamics Models
Pierre Magal (University of Bordeaux, France)
This presentation is devoted to bifurcation problems for some classes of PDE arising in the context of population dynamics. The main
difficulty in such a context is to understand the dynamical properties of a PDE with non‐linear and non‐local boundary conditions. A typical
class of examples is the so called age structured models. Age structured models have been well understood in terms of existence, uniqueness,
and stability of equilibria since the 80's. Nevertheless, up to recently, the bifurcation properties of the semiflow generated by such a system
has been only poorly understood. In this presentation, we will present with some results about existence and smoothness of the center
manifold in such a context.
To conclude the presentation, we will present a model for seasonal Influenza. We will present some analysis of Hopf bifurcations, and some
comparison between our model and real data coming from CDC in USA and ? réseau Sentinelles ? INSERM in France.
Harmonic analysis on quantum tori Quantum tori are fundamental examples
许全华（Université de Franche-Comté, France and 武汉大学）
In algebras of operators and noncommutative geometry. This talk will present a systematic study of harmonic analysis on quantum tori.
The results presented will include those on maximal inequalities, pointwise convergence of different summations, Fourier multipliers and Hardy
spaces. This is a joint work with Zeqian Chen and Zhi Yin.