大家好，本届学“数”论坛——学生专场的第一场报告来啦！本场报告类型为学术类，将于2024年3月21日14:00在数学学院二楼报告厅举办。主讲嘉宾为博士三年级雷子平同学、博士二年级谷晓玉同学。

雷子平同学师从我院葛化彬老师，主要研究方向是几何拓扑。本次报告题目为《双曲背景几何中关于全测地曲率的组合Calabi流》，报告内容主要如下：

In hyperbolic background geometry, we investigate a generalized circle packing (including circles, horocycles and hypercycles) with conical singularities on a surface with boundary, which has a total geodesic curvature on each generalized circle of this circle packing and a discrete Gaussian curvature on the center of each dual circle. The purpose of this paper is to find this type of circle packings with prescribed total geodesic curvatures on generalized circles and discrete Gaussian curvatures on centers of dual circles. To achieve this goal, we firstly establish existence and rigidity on this type of circle packings by the variational principle. Secondly,we introduce combinatorial Calabi flows and p-th combinatorial Calabi flows to find the circle packing with prescribed total geodesic curvatures on generalized circles and discrete Gaussian curvatures on centers of dual circles for the first time.

谷晓玉同学师从我院欧耀彬老师，主要研究方向是流体方程组的适定性和渐近奇异极限问题。本次报告题目为《三维有界区域中可压缩磁流体方程组的不可压及消失电阻系数极限》，报告内容主要如下：

In this paper, we prove the incompressible and non-resistive limit for the initial boundary value problem of isentropic compressible resistive magnetohydrodynamic (MHD) equations with ill-prepared initial data in three-dimensional bounded domains. We establish the high-order uniform estimates with respect to both the Mach number and the resistivity coefficient in the framework of new type of weighted Sobolev spaces. Then we obtain the strong convergence of the magnetic field and the divergence-free component of the velocity field, as both the Mach number and the resistivity coefficient tend to zero. There are two main difficulties. First, the 3D compressible MHD equations considered here has a more complicated structure than the Navier-Stokes equations or the 1D compressible MHD system. Second, under the ill-prepared assumption on the initial data, the rapidly oscillating waves will prevent us from taking the limit, and we cannot achieve strong convergence of the velocity. This talk is based on joint works with Prof. Yaobin Ou.

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