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The Ricci flow is a powerful tool in geometry to construct the canonical metric on a given manifold. It can be viewed as a nonlinear heat flow of the Riemannian metric and may develop finite time sing...
In this talk, we are mainly concerned with invariant geometric flows in affine-related geometries including centro-equiane, centro-affine, affine and affine-symplectic geometries. First, we show that ...
仿射Deligne-Lusztig簇是经典的Deligne-Lusztig簇在仿射旗流形中的类比,其几何性质在算术几何中有着重要的应用。本报告将介绍仿射Deligne-Lusztig簇与组合、算术几何、表示论等领域的联系,最新的进展,和一些公开问题。
In this talk, we apply Menke's JSJ decomposition for symplectic fillings to several families of contact 3-manifolds. Among other results, we complete the classification up to orientation-preserving di...
Shimura varieties are a class of algebraic geometric spaces that play a very important role in arithmetic geometry, especially in the Langlands program. In recent years, methods from the geometric rep...
The method of moving planes and moving quadrics expresses the implicit equation of a rational parametric surface as a compact determinant. Efficient computation of the moving planes and moving quadric...
I will present the joint work with Jialun Li and Pratyush Sarkar in the talk. As a final work to establish that the frame flows for geometrically finite hyperbolic manifolds of arbitrary dimensions ar...
几何表示论本世纪以来显得十分活跃,引起了越来越多的关注。本报告试图从这个方向的一些源头工作理解几何表示论的内涵。这些工作包括P. Deligne和G. Lusztig关于有限李型群的表示的工作,T.A. Springer关于Weyl群的表示的工作,D. Kazhdan和G.Lusztig关于Coxeter群与Hecke代数表示的工作等。
In this talk, we first briefly review history of the geometric singular perturbation theory, then talk about the traveling pulses for a diffusive Rosenzweig MacArthur model. We show the existence of t...
The classical Allard regularity says, a rectifiable varifold in the unit ball of the Euclidean space passing through the original point with volume density close to 1 and generalized mean curvature sm...
We obtain new mixed-norm estimates and geometric results on projections. In the proof we introduce a new quantity called s-amplitude, and interpolate analytically not only on p,q, but also on dimensio...
The problem of using covariates to predict shapes of objects in a regression setting is important in many fields. A formal statistical approach, termed geodesic regression model, is commonly used for ...
We will discuss two special cases of the three-dimensional Kakeya conjecture: SL_2 Kakeya and a refined Wolff's hairbrush result. As an application of the refined Wolff's hairbrush result, we will dis...
We will introduce the polynomial partitioning method which has wide applications in incidence geometry, geometric measure theory, and harmonic analysis. In the first course, we will present some basic...

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