Starting with the toy example of a star-shaped frame for the plane (e.g. sea star), we explain the powerful role operator-valued measure, and particularly coherent states (CS) can play in quantizing any set equipped with a measure. These integral quantizations are illustrated with the standard case involving the Weyl-Heisenberg group (yielding the canonical quantization), and with the case involving for affine group of the real line.

报 告 人：纪春岗 教授（南京师范大学数学科学学院）报告题目：Sums of Squares of Cyclotomic Fields时间：2013年1月17日（周四）上午10:00-11:00报告地点：致远楼105

The study of quasi-hereditary algebras has been a hot topic for about two decades in the circle of finite dimensional algebras. Interestingly, the notion of such algebras is first introduced by mathematicians working on algebraic groups, instead of those working on finite dimensional algebras. My talk will focus on why this happened. Thus, I shall explore the source of the theory of quasi-hereditary algebras in the representation theory of algebraic groups. That is, I shall show how highest weight categories appear naturally in representation theory of algebraic groups, leading to the definition of quasi-hereditary algebras.

报 告 人：马 力（河南师范大学特聘教授、博士生导师）报告题目：Non-local Heat Flows And Geometric Flows报告时间：2013年1月18日（周五）下午4:00-5:00报告地点：致远楼107

Data assimilation problems consist in retrieving the value of the solution at some time (everywhere in the domain) for an evolution problem knowing informations on the solution on a subdomain during a period of time. In a classical approach one tries to find the initial data using a Tychonov regularisation. This depends on a regularisation parameter and the problem becomes ill-posed when this parameter tends to zero. We will present a non standard approach, based on Controllability techniques, which enables to retrieve the solution at the final time. A consequence is also to give a sense to the classical approach in a non standard functional class. We will present this method on the heat equation for simplicity and if time permits some other example on a large scale ocean model with numerical tests. Prof. Jean-Pierre Puel Laboratoire de Mathematiques de Versailles Universite de Versailles St Quentin

Let be the set of matrices over a field F. Consider a graph G = ( , ) with as the vertex set such that two vertices A, B are adjacent if rank (A-B)=1. We study graph properties of G when F is a finite field. In particular, we show that G is a regular connected graph with diameter equal to min{m,n}; it is always Hamiltonian; it is Eulerian if and only if F has an odd number of elements.Furthermore,we determine the independence number,chromatic number and clique number of G. These results are used to characterize the graph endomorphisms of G, which extends Hua's fundamental theorem of geometry on .

I will briefly introduce two books and will talk about one of the problems---the realisation problem---discussed in the books.

报告人：陆国震教授 (北京师范大学, 美国韦恩州立大学)题目： Affine Moser-Trudinger and Adams inequalities and applications to PDEs时间：2013年1月3日(星期四)上午10：00—11：00地点：数学系致远楼10