Hecke endomorphism algebras are a natural generalisation of q-Schur algebras associated with symmetric groups to arbitrary Coxeter groups. These algebras attract a worldwide attention for many years. For example, B. Parshall, L. Scott and the speaker (DPS) investigated some stratification structure of those associated with Weyl groups twenty-years ago with a motivation of applying them to representations of finite groups of Lie type. Recently, these algebras play an important role in Williamson’s singular bimodule theory, while H. Bao, J. Kujawa, Y. Li and W. Wang investigated a type of Schur-Weyl duality involving Hecke endomorphism algebras of type B,C, or D. In this talk, I will talk about a DPS conjecture and discuss a new approach to get is resolved. In particular, I will explain how exact categories are used in this approach.

渐近分析是数学分析里的一个重要分支，它在计算机，物理，应用数学等领域有着广泛的应用。它能够很好地描绘许多特殊函数的极限行为，是研究常微分，偏微分方程解的重要的工具。早在18世纪，英国天文学家George Biddell Airy就将渐近分析应用于对彩虹的研究，从而得到了著名的Airy积分。时至今日，渐近分析的方法在一些尖端的科学研究中仍然起着举足轻重的作用，例如在对于海啸的研究中，Michael Berry利用渐近分析的方法，得到了海啸模型的近似解。比起其它的计算方法，Michael Berry的方法大大地提高了计算机模拟的速度，从而体现了渐近分析的优越性。本次报告将从彩虹、海啸这些人们熟悉的现象出发，带领大家一起探索渐近分析的奥秘。

在调查一个群体的收入时, 很多时候会出现被调查者拒绝回答或者回答不真实的情况. 这一现象在收入过高或者过低这两个极端情况时越发明显. 对于数据不完整的情况, 从已有的文献看来, 通常的做法是将问题假设为数据是左截断右删失模型. 对其处理的基本思路是借用生存分析中的PL估计等方法, 先估计出分布函数F, 然后利用分布 函数和Lorenz曲线之间的关系估计出Lorenz曲线. 而本报告处理数据缺失的情形, 这样做可以符合调查实际更多情况. 直观上, 我们可以想象, 这样的调查结果是有偏差的. 由于缺失了高收入或低收入者的回答, 这样的偏差会导致对个体间收入差距的估计偏小, 反映到对基尼系数的影响时就体现为单纯依据样本计算出的基尼系数会比真实的基尼系数偏小. 因此, 仅仅是使用那些回答者的样本是不够的, 我们需要再加上缺失机制等信息, 尽可能地将原始的情况恢复出来. 假定数据缺失机制与收入水平有关, 即假定不回答的概率与被调查者的收入有关. 在几种不同的收入分布模型和缺失机制下研究了基尼系数的估计问题. 模拟研究表明在假定了缺失机制下对基尼系数的估计更加准确。

We propose a structured integro-difference equation model for an invasive marine species with a pelagic larval stage and examine the role of dispersal heterogeniety on the spreading speed. The spread of the green crab up the northwest coast of the Atlantic is used as a case study. We find that the relationship between spreading speed and demographic and dispersal parameters is similar to the relationship found in Fisher's equation. We also find that temporal variation in dispersal results in a faster spread rate

研究了斑块环境下种群(人群)的迁移对于疾病传播或者物种数量动态变化规律的影响，分析了上述定性结果在基于斑块控制策略的疾病控制及物种保护中的应用，上述报告基于与王新新、张巍巍、芦雪娟以及王林教授等人合作成果。

In this talk, we will discuss the Ringel-Hall algebras of a hereditary abelian category. From the category of the $/mathbb{Z}/2$-graded complexes over a hereditary abelian category, we consider a certain quotient algebra and some localization of its Ringel-Hall algebra, which is called the modified Ringel-Hall algebra. When this hereditary abelian category is finitary, in particular the category of representations of a quiver and the category of coherent sheaves on a weighted projective line over a finite field, we prove that the modified Ringel-Hall algebra is isomorphic to the Drinfeld double of the extended Ringel-Hall algebra of the hereditary abelian category.

To study the well-known Schneider's projection problem, Lutwak, Yang and Zhang introduced a U-functional for polytopes, and posed two conjectures for this U-functional. In this paper, an affirmative answer for the second conjecture is given. As a by-product to prove our main theorem, a new sharp affine inequality characterizing simplices is established for the centered cone-volume measures.

We consider some sets of points whose codings have prescribed group frequencies and determine their Hausdorff dimensions. These sets can be used to describe orbit properties of some maps in the view of dynamical way. We shall also introduce some basic knowledge of fractals.