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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The logarithmic Brunn-Minkowski inequality conjecture in convex geometry
凸几何 对数 布伦-闵可夫斯基 不等式猜想
2023/4/21
The logarithmic Brunn-Minkowski inequality conjecture is one of the most intriguing challenges in convex geometry since 2012. Notably, this conjectured inequality is stronger than the celebrated Brunn...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Gauss-Bonnet formula beyond the aspherical conjecture
超越非球面猜想 Gauss-Bonnet 曲面
2023/4/21
In this talk, I'll make a discussion on recent progress in the research of scalar curvature. I'll review the backgrounds from Gauss-Bonnet formula to the aspherical conjecture, and then focus on the f...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some special cases of the three dimensional Kakeya conjecture and their application to the restriction conjecture
三维Kakeya猜想 特殊情况 限制猜想
2023/5/9
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...
The Gronwall conjecture states that a planar 3-web of foliations which admits more than one distinct linearizations is locally equivalent to an algebraic web. We propose an analogue of the Gronwall co...
The Log-Convex Density Conjecture and vertical surface area in warped products
The Log-Convex Density Conjecture vertical surface area warped products Differential Geometry
2011/9/19
Abstract: We examine the vertical component of surface area in the warped product of a Euclidean interval and a fiber manifold with product density. We determine general conditions under which vertica...
Concerning the Strauss conjecture on asymptotically Euclidean manifolds
Strauss conjecture KSS estimates weighted Strichartz estimates
2010/11/30
In this paper we verify the Strauss conjecture for semilinear wave equations on asymptotically Euclidean manifolds when n = 3, 4, we also give an almost sharp life span for the subcritical case 2 p ...
Manin's Conjecture for a Singular Sextic del Pezzo Surface
Manin's Conjecture Singular Sextic del Pezzo Surface
2010/12/6
We prove Manin’s conjecture for a del Pezzo surface of de-gree six which has one singularity of type A2. Moreover, we achieve a meromorphic continuation and explicit expression of the associated heigh...
A note on the Bloch-Beilinson conjecture for K3 surfaces and spherical objects
Bloch-Beilinson conjecture K3 surfaces spherical objects
2010/12/10
For a projective K3 surface X over an algebraically closed field k let Db(X) denote the bounded derived category of coherent sheaves. Spherical objects, e.g. line bundles and rigid
stable bundles, pl...
Evidence for a conjecture of Pandharipande
conjecture of Pandharipande enumerative geometry
2010/3/1
In his paper ``Hodge integrals and degenerate contributions'', Pandharipande studied the relationship between the enumerative geometry of certain 3-folds and the Gromov-Witten invariants. In some good...
The Fibered Isomorphism Conjecture for Complex Manifolds
Complex projective variety Complex surfaces Whitehead group Fibered isomorphism conjecture Negative $K$-groups
2007/12/11
In this paper we show that the Fibered Isomorphism Conjecture of Farrell and Jones, corresponding to the stable topological pseudoisotopy functor, is true for the fundamental groups of a class of comp...