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The classical isoperimetric problem was known in the Ancient Greek. But the rigorous mathematical proof appeared late till the 19th century. Late works showed that the isoperimetric inequality was equivalent to the analytic Sobolev inequality. Is there an analytic inequality that is equivalent to the Brunn-Minkowski equality? We will discuss this problem.

This paper considers a class of bistable reaction-diffusion equations in the plane. We will focus on the multiplicity, shape and attractivity of the heterogeneous steady states for bistable reaction-diffusion equation in the plane.

题目：The Applications of Tensor Eigenvalues, Positive Semi-Definite Tensors and Copositive Tensors in Physics.报告人：祁力群教授 香港理工大学时间: 2016年12月6日(周二)下午16:00地点: 致远楼107室祁力群教授简介：中国著名数学家。男，江苏扬州人，1984年毕业于美国威斯康星大学计算机科学系，获博士学位。现任香港理工大学应用数学系教授，博士导师。是澳大利亚Curtin科技大学研究教授，俄罗斯Petrovskaya 科学与艺...

We present a simple model that describes ovarian tumor growth and tumor induced angiogenesis, subject to on and off anti-angiogenesis treatment. The tumor growth is governed by Droop’s cell quota model,a mathematical expression developed in ecology. Here, the cell quota represents the intracellular concentration of necessary nutrients provided through blood supply. We present mathematical analysis of the model, including some local and global stability results.

In this talk, we propose and analyze an epidemic model with relapse, infection age, and a general nonlinear incidence rate. Established is a threshold dynamics determined by the basic reproduction number R0. Roughly speaking, if R0 < 1 then the disease-free steady state is globally asymptotically stable while if R0 > 1 then the endemic steady state is globally asymptotically stable. The global attractivity for the steady states are obtained by employing the fluctuation lemma and the approach of Lyapunov functionals,

In this talk, we will introduce some models which have Bogdanov-Takens singularity, and discuss if the models can undergo Bogdanov-Takens Bifurcation.

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。