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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A simpler proof of the Frank-Lieb inequality on the Heisenberg group
海森堡群 Frank-Lieb inequality 更简单证明
2023/4/14
I will discuss the Hardy-Littlewood integral inequality with sharp constant on the Heisenberg goup proved by Frank and Lieb. I will outline a simpler proof which bypasses the sophisticated argument fo...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Berndtsson’s proof of the Bourgain-Milman theorem
伯恩松 布尔根-米尔曼定理 证明
2023/4/28
I will give a report on the Bourgain-Milman theorem. Berndtsson used complex methods to give a proof. I’ll talk about his papers. However, the best constant for the Bourgain-Milman theorem is still un...
“Magic-angle” trilayer graphene may be a rare, magnet-proof superconductor（图）
三层石墨烯 防磁超导体 MRI机器 量子计算机
2023/6/7
MIT physicists have observed signs of a rare type of superconductivity in a material called magic-angle twisted trilayer graphene. In a study appearing today in Nature, the researchers report that the...
A SHORT PROOF OF ROST NILPOTENCE VIA REFINED CORRESPONDENCES
ROST NILPOTENCE VIA REFINED CORRESPONDENCES
2015/9/29
I generalize the standard notion of the composition g ◦f of
correspondences f : X → Y and g : Y → Z to the case that X and Z are
arbitrary varieties but Y is smooth and projective. Using this ...
A PROOF OF THE KAZHDAN-LUSZTIG PURITY THEOREM VIA THE DECOMPOSITION THEOREM OF BBD
KAZHDAN-LUSZTIG DECOMPOSITION
2015/9/29
The ˉrst ingredient is quite deep, and we will not say anything much about its
proof, using it simply as a \black box". The second ingredient is elementary, and
we take this opportunity to present a...
A PROOF OF THE UNIFORMIZATION THEOREM FOR ARBITRARY PLANE DOMAINS
UNIFORMIZATION THEOREM ARBITRARY PLANE DOMAINS
2015/8/26
We present a simple constructive proof of the Uniformization Theorem which works for plane domains. The proof is a combination of covering space theory and Koebe's constructive proof of the Riemann ma...
A proof of Thurston's topological characterization of rational functions
Thurston's topological characterization rational functions
2015/8/26
The criterion proved in this paper was stated by Thurston in November 1982. Thurston lectured on its proof on several occasions, notably at the NSF summer conference inDuluth, 1983, where one of the a...
In this paper we will give a proof of Kolmogorov’s theorem on the conservation of invariant tori. This proof is close to the one given by Bennettin, Galgani, Giorgilli and Strelcyn in [2]; we follow t...
A Simple Proof of the Ahlswede-Csiszk One-Bit Theorem
Simple Proof Ahlswede-Csiszk One-Bit Theorem
2015/8/12
It is proved that if (X, Y) are two finite alphabet correlated sources with p(x, JJ) > 0 for all (x, v) E (XX g), and if a function F(X, Y) is a-sensitive, then the rate R of transmission from X to Y ...
A short proof of the logarithmic Bramson correction in Fisher-KPP equations
logarithmic Bramson correction Fisher-KPP equations
2015/7/14
In this paper, we explain in simple PDE terms a famous result of Bramson about the logarithmic delay of the position of the solutions u(t, x) of Fisher-KPP reaction-diffusion equations in R, with resp...
Anisotropic interactions in a first-order aggregation model:a proof of concept
Anisotropy visual perception aggregation models implicit equations regularization relaxation time uniqueness criteria singular perturbation
2015/7/14
We extend a well-studied ODE model for collective behaviour by considering anisotropic interactions among individuals. Anisotropy is modeled by limited sensorial perception of individuals, that depend...
A SHORT PROOF OF THE CONJECTURE WITHOUT GROMOV-WITTEN THEORY: HURWITZ THEORY AND THE MODULI OF CURVES
HURWITZ THEORY THE MODULI OF CURVES
2015/7/14
I. P. GOULDEN, D. M. JACKSON AND R. VAKILConjecture. The
approach is through the Ekedahl-Lando-Shapiro-Vainshtein theorem, which establishes the \polynomiality" of Hurwitz numbers, from which we pick...
A SHORT PROOF OF THE CONJECTURE WITHOUT GROMOV-WITTEN THEORY: HURWITZ THEORY AND THE MODULI OF CURVES
HURWITZ THEORY THE MODULI OF CURVES
2015/7/14
I. P. GOULDEN, D. M. JACKSON AND R. VAKILConjecture. The
approach is through the Ekedahl-Lando-Shapiro-Vainshtein theorem, which establishes the \polynomiality" of Hurwitz numbers, from which we pick...
Let k be a eld, and let G be an algebraic group over k, by which we mean a connected smooth k-group
scheme (not necessarily ane). Recall that such a G is automatically separated, nite type, and ge...
A Proof of the Stability of the Spectral Difference Method for All Orders of Accuracy
Spectral Difference Method Accuracy
2015/6/23
One of the most promising approaches is the
Discontinuous Galerkin (DG) method, for which the theoretical basis has been provided in
a series of papers by Cockburn and Shu [1, 2, 3, 4]. The rapid gr...