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.

题目：Judicious Partitions of Graphs报告人：Professor Xingxing Yu （School of Mathematics Georgia Institute of Technology）地点：致远楼105室时间：2017年7月11日(周二)上午10:00欢迎大家前往参加

We characterize common reducing subspaces of several weighted shifts with operator weights. As applications, we study the common reducing subspaces of the multiplication operators by powers of coordinate functions on Hilbert spaces of holomorphic functions in several variables. The identification of reducing subspaces also leads to structure theorems for the commutants of von Neumann algebras generated by these multiplication operators. This general approach applies to weighted Hardy spaces, weighted Bergman spaces, Drury-Arveson spaces and Dirichlet spaces of the unit ball or polydisk uniformly.

Solving the Poisson/Poisson-Boltzmann (PB) equation with varying coefficients has been a bottleneck for simulating proteins within the framework of implicit solvent model due to the dielectric inhomogeneity. In this talk, we will present our recent work on a numerical Boundary Integral Equation (BIE) method for calculations of electrostatic fields in systems consisting multiple proteins in solvent. The BIE is further coupled with treecode for fast kernel summation, and is applicable to arbitrary shaped dielectric interface. Numerical results about the accuracy and efficiency will be discussed, we also show interesting phenomenon that the induced charge on the dielectric interfaces can significantly change the interaction energy of solvated proteins.