学术报告题目和摘要

报告人：董久刚

报告题目：Cucker-Smale Flocking Under General Interaction Topologies

报告摘要：In the literature, the study of the Cucker-Smale (C-S) model is all restricted to several special interaction topologies. In this talk, we consider the flocking behavior of the C-S model under general interaction topologies, which contain all existing topology structures in relation to the C-S model as special cases. In particular, the topology with multiple leaders is included. The flocking results are guaranteed under some conditions on the system parameters and the initial states only. The critical exponent below which unconditional convergence holds is given, depending only on the interaction topology. It is consistent with the ones obtained with some known special topologies in the literature. The convergence results are shown by employing a new combination of perturbation method and algebraic graph theory.

报告人：房祥东

报告题目：Existence of solutions for a quasilinear Schrodinger equation

报告摘要：In recent years, the quasilinear Schrödinger equation has been studied extensively. In this talk, we will discuss the existence of the ground state solution with an asymptotic condition at infinity, and then we will focus on

infinitely many geometrically distinct solutions by the improved generalized

Nehari manifold.

报告人：郭潇

报告题目：《线性代数与空间解析几何》教学与考试方式的改革

报告摘要：针对《线性代数与空间解析几何》这门课程概念抽象，内容多，时间紧的特点，提出关于多媒体课件的应用，网络资源的利用，添加应用实例等教学改革方案。针对授课对象为大一新生，基础不均衡的特点，开展考察方式多样、多次，可以舍去最低分等考试改革尝试。结合员工的表现，讨论教学及考试改革方案的优缺点。

报告人：石振锋

报告题目：应用问题驱动的数学与计算机教学

内容简介：基于数学系专业本科生培养目标及课程体系的思考，通过几个案例说明如何从实际工程应用背景出发，提炼数学科学问题，提出科学的解决方案和实现虚拟仿真的过程。同时对基于应用问题驱动的启发式数学教学方法也进行案例说明。

报告人：王振

报告题目：分层流体内波的生成演化

报告摘要：在流体表面有各种各样的波浪形态， 而流体内部也会由于密度的不同而形成内部波动，即内波，内波相对于表面波来说由于观察不方便，相对更隐蔽，但其造成的破坏作用更剧烈。在密度层化流体中由于地形的作用和外部扰动等因素是内波生成的主要原因。我们目前关注两层流体的内波生成，演化的规律，通过理论分析和数值模拟对其进行了解。

报告人：杨畅

报告题目: Mixed semi-Lagrangian/finite difference methods for plasma simulations

报告摘要: In this paper, we present an efficient algorithm for the long time behavior of plasma simulations. We will focus on 4D drift-kinetic model, where the plasma's motion occurs in the plane perpendicular to the magnetic field and can be governed by the 2D guiding-center model.

Hermite WENO reconstructions are applied for solving the Vlasov equation. Here we consider an arbitrary computational domain with an appropriate numerical method for the treatment of boundary conditions.

Then we apply this algorithm for plasma turbulence simulations. We first solve the 2D guiding-center model in a D-shape domain and investigate the numerical stability of the steady state. Then, the 4D drift-kinetic model is studied with a mixed method, i.e. the semi-Lagrangian method in linear phase and finite difference method during the nonlinear phase.

Numerical results show that the mixed method is efficient and accurate in linear phase and it is much stable during the nonlinear phase. Moreover, in practice it has better conservation properties.

报告人：尹逊波

报告题目：《工科数学分析教学与考试方法改革实践

报告摘要：主要介绍教学改革的MOOC课程建设情况及考试方法改革中的的机考及网上阅卷两项改革的实施情况。

报告人：张超

报告题目：Note on Non-i.i.d. Statistical Learning Theory

报告摘要：In this talk, we will go through some results on the statistical learning theory in the non-i.i.d. scenario. In particular, we first brief some classical results of statistical learning theory. Then, a theoretical analysis of domain adaptation will be given. Next, we will study the generalization bound of the learning process in the setting of stochastic-process sampling including Levy processes and continuous-time Markov chains.

报告人：张文龙

报告题目：快速收敛的pi级数