In this talk, we first introduce the quasitriangular Hopf algebras, the Drinfeld doubles of finite dimensional Hopf algebras, and their representation theory. Then we introduce the cocycle deformation theory of Hopf algebras. Finally, we introduce Taft algebras, their Drinfeld doubles and their representation theory and Green rings.

This paper develops an asymptotic theory for general nonlinear regression models, establishing a new framework on least squares estimation that is easy to apply for various nonlinear regression models with heteroscedasticity. This paper explores an application of the framework to nonlinear regression models with nonstationarity and heteroscedasticity. Accompanying with these main results, this paper provides a maximum inequality for a class of martingales and establishes some new results on convergence to a local time and convergence to a mixture of normal distributions, which are interested in their own rights.

题目：极小曲面纵横谈报告人：忻元龙 教授（复旦大学数学科学学院）时间：2018年12月7日（周五）16:00-17:00地点：致远楼101室欢迎广大师生参加

It is well-known that the R-matrix presentation of the Yangian in type A yields generators of its Drinfeld presentation. It has been an open problem since Drinfeld's pioneering work to extend this result to the remaining types. We will provide a solution for the classical types of BCD by constructing an explicit isomorphism between the R-matrix and Drinfeld presentations of the Yangian

In this talk, I will consider the endomorphism algebra of projective-injective module over a finite dimensional algebra. In several different context (e.g., (parabolic) BGG category O, quantum groups, rational Cherednik algebras, etc), it has been proved or conjectured that this endomorphism algebra can always be endowed with a symmetric structure. I will report our recent progress in this direction which are based on a joint work with Ngau Lam and a joint work with Ming Fang.

The theory of cluster algebras was set up by Fomin and Zelevinsky in a series of articles in 2001 and the next few years. In these references, they proposed some problems and conjectures on cluster algebras. In this talk, we will mention the progress of the positivity conjectures of cluster variables and d-vectors, the conjectures on sign-coherence of c-vectors and g-vectors, the problems of F-polynomials and g-vectors, the uniqueness of seed under mutation equivalence and the totality of sign-skew-symmetric matrices, the unistructurality of cluster algebras, etc.

In this talk, a brief review will be given for the insurance risk theory. Some recent results on optimal control of reinsurance, investment and dividend with various objectives will be presented. Different approaches to solve the optimality problems will be discussed and optimal strategies are analyzed. Specifically, some mean-variance optimal control problems are to be discussed in some detail.