报告题目：Heat kernel estimate

报 告 人：胡家信

时 间：2024年11月25日（周一） 下午 15:00-17:00

地 点：国交2号楼 315会议室

简 介：The heat kernel, also called the probability transition function, is an important concept in analysis and probability. Basically, a heat kernel associated with a Brownian motion on the manifold or on the Euclidean space admits a Gaussian estimate. However, the situation is significantly different on the fractal. In this talk, I will explain this phenomenon, and give the equivalence characterizations for heat kernel estimates for any resurrected regular Dirichlet forms on fractals.

报告题目：数学物理及偏微分方程国际系列论坛 (12) ：Hidden convexi…

报 告 人：Professor Nassif Ghoussoub

时 间：Beijing time: 10:30-11: 30 am, Nov.15th (Friday),2024

地 点：国交2号楼315会议室

简 介：We study compressible and incompressible nonlinear elasticity variational problems in a general context. Our main result gives a sufficient condition for an equilibrium to be a global energy minimizer, in terms of convexity properties of the pressure in the deformed configuration. We also provide a convex relaxation of the problem together with its dual formulation, based on measure-valued mappings, which coincides with the original problem under our condition.

报告题目：数学物理及偏微分方程国际系列论坛（11）： Minimizing th…

报 告 人：Professor Eric Sere

时 间：Beijing time: 16: 00--17: 00 pm, Nov. 12th (Tuesday), 2024

地 点：Zoom Meeting ID: 626 871 3564, Passcode: 2024

简 介：This talk is based on joint works with J. Dolbeault, M.J. Esteban and M. Lewin. Consider an electron moving in the attractive Coulomb potential generated by a positive finite measure representing an external charge density. If the total charge is fixed, it is well known that the lowest eigenvalue of the corresponding Schrodinger operator is minimized when the measure is a delta. We investigate the conjecture that the same holds for the relativistic Dirac-Coulomb operator. First we state an abstract result on symmetric operators with gaps. Applied to Dirac-Coulomb operators, this result gives conditions ensuring the existence of a natural self-adjoint realisation and that its eigenvalues are given by min-max formulas Then we define a critical charge such that, if the total charge is fixed below it, then there exists a measure minimising the first eigenvalue of the Dirac-Coulomb operator. We find that this optimal measure concentrates on a compact set of Lebesgue measure zero. The las...