For the time-fractional phase field models, the corresponding energy dissipation law has not been well studied on both the continuous level and the discrete level. In this talk, we shall address these open issues. More precisely, we prove that the time-fractional phase field models indeed admit an energy dissipation law of an integral type. In the discrete level, we propose a class of finite difference schemes that can inherit the theoretical energy stability. Our discussion covers the time-fractional gradient systems, including the time-fractional Allen-Cahn equation, the time-fractional Cahn-Hilliard equation, and the time-fractional molecular beam epitaxy models. Moreover, a numerical study of the coarsening rate of random initial states depending on the fractional parameter $/alpha$ reveals that there are several coarsening stages for all the three models, while there exist a $-/alpha/3$ power law coarsening stage for both

The Dynkin Diagram and the Stiefel Diagram are ”visualizations” of Lie groups (or their root systems) which are very familiar to geometers and topologists. We propose an ”enhanced” Coxeter Plane as a third visualization. This has a purely Lie-theoretic definition, but it arises most naturally from a certain isomonodromic family of meromorphic connections, constructed as a special case of the Toda equations - an integrable system. This is joint work with Nan-Kuo Ho.

In this talk, we first recall the Donaldson- Uhlenbeck-Yau theorem which states that Hermitian-Einstein equation must be solvable on a stable holomorphic vector bundle, and introduce our recent works on the Hermitian-Einstein equation, Bogomolov type inequality and the Hermitian Yang- Mills flow.

we develop a global geometric method to study variations of complex structures over Kahler manifolds. More precisely, by using operators from Hodge theory on a complete Kahler manifold, we obtain closed formulas for holomorphic canonical forms under global variations of complex structures and present several applications including solving the general Belrtami equations and the Kuranishi obstruction equations in deformation theory of complex structures.

Suppose we have a zeta function (Dirichlet series) which satisfies a standard functional equation. A classical method of Landau gives an estimate of the partial sum of its coefficients with a power saving error term. In this talk, I will explain a uniform version of Landau's theorem; the implied constant in the error term will depend only on the `shape' of the functional equation. I also would like to discuss several applications of this result. This is a joint work with David Lowry-Duda and Frank Thorne.

题目：Minsum Location Extended To Gauges And To Convex Sets报告人：Professor Horst Martini（德国开姆尼茨科技大学）地点：宁静楼104室时间： 2018年8月24日（周五）下午16：00-17:30欢迎广大师生参加

In this talk, I will present the global existence and decay rates of the solutions near Maxwellian for non-linear Fokker--Planck equations and non-linear Vlasov–Poisson–Fokker–Planck equations. The global existence is proved by combining uniform-in-time energy estimates and local solution constructed by Picard type iteration sequence. The decay rates of the nonlinear model is obtained by using the precise spectral analysis of the linear Fokker--Planck operator as well as the energy method. The nonlinearity in the model brings new difficulty for the energy estimates, which is resolved by additional tailored weighted-in-$v$ energy estimates suitable for Fokker--Planck operators.

Inspired by the work of Douglas and Foias in 2006 on the structure of the square of a C0(1) operator, we form a conjecture about a certain reducibility of any power N of a C0(1) operator. We then prove this conjecture for N = 3 by determining explicitly the relevant reducing subspaces.