As we know, there are differences in travel frequency among people by age, ethnicity, region, gender, income, etc. Usually only a small fraction of people are frequent travelers while most travel occasionally or never. For instance, the percentages of frequent air traveler, occasional air traveler, and never flown in the U.S. in 2015 are 7%, 71%, and 22%, respectively. In this talk, we propose a multipatch epidemic model to investigate the effect of travel behavior on the spread of infectious diseases.

在本次报告中,我们将首先回顾经典Navier-Stokes方程的正则性结果，而后介绍我们在3维各向异性的navier-Stokes方程方面的适定性结果；最后介绍我们最近有关3维经典Navier-Stokes方程的一个分量的临界正则性准则。

In this paper, two decoupled finite element methods are proposed for solving the 3D primitive equations of ocean. Based on the finite element approximation, optimal error estimates are given under the convergence condition. And the detailed algorithms are given in the section of numerical tests. Further, numerical calculations are implemented to validate the theoretical analysis and more calculations are implemented for a more meaningful problem. For both theoretical and numerical points of view, the proposed decoupled finite element methods are the effective strategies to solve the 3D primitive equations of ocean.

The endoplasmic reticulum (ER) in plant cells forms a highly dynamic network of complex geometry. ER network morphology and dynamics are influenced by a number of biophysical processes, including filament/tubule tension, viscous forces, Brownian diffusion and interactions with many other organelles and cytoskeletal elements. Previous studies have indicated that ER networks can be thought of as constrained minimal-length networks acted on by a variety of forces that perturb and/or remodel the network. Here, we study two specific biophysical processes involved in remodelling.

Dirichlet character plays an important role in number theory. Almost 100 years have passed since the fundamental contribution of G. Polya and I.M. Vinogradov (1918), there were very few substantial progress like D.A. Burgess's work in late 1950s. The past decade has seen many promising changes due to the success of new ideas and tools. In this talk, some old and new results and several open problems in the field of character sums will be presented. Also I will introduce the joint works with Profs. C.H. Jia and M.A. Korolev.

This talk will discuss the modular category for a vertex operator subperalgebras and its connection with the 16-fold way conjecture in category theory. The is a joint work with Richard Ng and Li Ren.

复合材料已广泛应用于航天航空、土木工程和日常生活中，对于复合材料的热学性质和力学性质的研究日益趋于成熟。对具有周期孔洞结构的热力耦合复合材料，通过研究等效性能去分析复合材料所具有的性能特点，进一步优化材料性能。这类复合材料问题，数学上可借助局部具有剧烈振荡系数的偏微分方程边值问题进行刻画，具有小周期性和强耦合性。此类问题的多尺度渐近分析对于预测这类复合材料的等效性能具有重大影响和深远意义。首先，本文针对具有周期孔洞结构的热力耦合复合材料问题，提出了一种三重尺度渐近形式展开。考虑微观、介观、宏观之间的联系，通过三重尺度方法，求解了构成形式展开解的单胞函数。

In 1994, I.Kan constructed a smooth map on the annulus admitting two physical measures, whose basins are intermingled. In this talk, we will show that all these Kan's maps are C^2-robustly topological mixing. This shows the topological and the ergodic notions of indecomposability are strikingly different: these maps are topological mixing, yet admit two different physical measures. This is a joint work with Shaobo Gan.