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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
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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
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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...
A SHORT PROOF OF ROST NILPOTENCE VIA REFINED CORRESPONDENCES
ROST NILPOTENCE VIA REFINED CORRESPONDENCES
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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
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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
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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
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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...
A PROOF OF KOLMOGOROV’S THEOREM
KOLMOGOROV’S THEOREM
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2015/8/26
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
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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
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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
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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
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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
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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 MODERN PROOF OF CHEVALLEY'S THEOREM ON ALGEBRAIC GROUPS
MODERN PROOF ALGEBRAIC GROUPS
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2015/7/6
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...
Proof of Riemann hypothesis
even prime number odd prime number non-trivial zero point.
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2015/6/2
Let Re(s)﹦π(n)／n,(n﹦2), and Im(s)﹦((π(n)﹣π(2))㏒n)i,(n＞2)， Riemann hypothesis is proved.
Combinatorial Proof of the Inversion Formula on the Kazhdan-Lusztig R-Polynomials
Kazhdan-Lusztig R-polynomial inversion formula Bruhat order
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2014/6/3
In this paper, we present a combinatorial proof of the inversion formula on the Kazhdan-Lusztig R-polynomials. This problem was raised by Brenti. As a consequence, we obtain a combinatorial interpreta...