Kaehler metrics with large symmetry on a toric manifold correspond to a class of convex functions on the whole euclidean space. This allows us to use more special techniques from convex analysis in the study of Kaehler geometry on toric manifolds. In this talk, we will first discuss various approaches in the study of Kaehler-Einstein metrics on toric Fano manifolds. Then we discuss some recent work, in particular on Kaehler-Ricci flow on G-manifolds by the method used for toric manifolds. Some questions/problems are also discussed.

对数凹(log-concave)这个概念在凸几何与泛函不等式的研究中扮演着重要的角色。报告人将从对数凹测度谈起，结合最优传输理论，介绍随机局部化方法在泛函不等式研究中的应用。

We establish the validity of the Euler+Prandtl approximation for solutions of the Navier-Stokes equations in the half plane with Dirichlet boundary conditions, in the vanishing viscosity limit, for initial data which are analytic only near the boundary, and Sobolev smooth away from the boundary. Our proof does not require higher order correctors, and works directly by estimating an L1 -type norm for the vorticity of the error term in the expansion Navier-Stokes−(Euler+Prandtl). An important ingredient in the proof is the propagation of local analyticity for the Euler equation, a result of independent interest.

In this talk, we will study C^{1, 1} regularity for solutions to the degenerate Lp Dual Minkowski problem and the existence of the smooth solution to the Gauss image.腾讯会议号：131-965-267会议链接：https://meeting.tencent.com/dm/iD9IGmFJEu19 All are ...

In this talk, by using new auxiliary functions, we study a class of contracting flows of closed, star-shaped hypersurfaces in R^n+1 with speed $r^{\frac{\alpha}{\beta}} \sigma_k^{\frac{1}{\beta}}$, where $\sigma_k$ is the $k$-th element...

In this talk, we will first introduce some classical topics concerning the geometry of minimal surfaces in R^n. Then we will discuss the Bernstein type theorems and Gauss-Bonnet type formula for minimal surfaces in R^3 or R^n...

In this talk we discuss an existence result regarding bounded-energy weak-solutions for the quasi-stationary compressible Stokes equations. This system arises for instance in biology, porous media, supra-conductivity or other applications in the low Reynolds number regime. These equations are formally obtained from the Navier-Stokes system for a compressible barotropic fluid by discarding the convective terms from the momentum equation.

We present a method to study global strong solutions of partially dissipative hyperbolic systems in a critical regularity setting. Introducing hybrid Besov norms, with different regularity exponents in low and high frequency, we pinpoint optimal smallness conditions for global well-posedness and get more accurate information on the qualitative properties of the constructed solutions.To handle the high frequencies of the solution, our analysis relies on the construction of a Lyapunov functional in the spirit of the one constructed by Beauchard and Zuazua (ARMA 2011). And concerning the low frequencies, exhibiting a damped mode with faster time decay than the whole solution plays a key role.