报告人：韩永生 教授   奥本大学

题目：Singular integral and geometry
报告语言：中文&英文

时间：2023.05.06 15：30-16：30

地点：MCM110

摘要：The geometric considerations enter in a decisive way in many questions of harmonic analysis. For example, the estimation of the Fourier transform of surface-carried measure, which played a key role in averages over lower-dimensional varieties, restriction theorems, in connection with the study of Fourier integral operators, and in applications to linear and non-linear dispersive equations.
In this talk, our focus will be on singular integral and the geometry that describe the singularities of the kernels of these operators, and which controls the releveant estimates that are made. The kind of geometry that arises is local in nature and is based on a distance = d(x, y). This metric controls what happens when y is near x. However, the exact size of d(x, y) is not crucial but what matters is the order of magnitude of d as y → x. 
We will describe how distants deduce the singular integrals in the Euclidean space; spaces of homogeneous type in the sense of Coifman and Weiss, and the Dunkl setting which is associated with finite reflection groups on the Euclidean space.

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报告人: 颜立新 教授 (中山大学)
题目: Harmonic analysis meets wave equation

报告语言：中文&英文

时间: 2023.05.09 10:00-11:00 
地点: N913
摘要: In this talk I plan to survey some progress on Hardy and BMO spaces, Riesz transforms, Bochner-Riesz means and spherical means by using the method of wave equation,and show interesting connections and interaction of different fields such as harmonic analysis, functional analysis and PDE. 

（报告人简介：颜立新，教授，博士生导师，国家杰出青年基金获得者, 国务院政府特殊津贴专家。 1996年中山大学数学系博士毕业后留校任教，2004年晋升教授。曾先后入选教育部新世纪优秀人才支持计划，国家杰出青年基金资助， 2018年度教育部自然科学奖一等奖（第一完成人）。主要从事调和分析领域的研究，已在 J. Amer. Math. Soc., Comm. Pure Appl. Math., Memoirs of AMS, Math. Ann.等数学期刊发表学术论文九十余篇。）

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报告人：杨开 （重庆大学）
题目: Solitons and Breathers in the modulus KdV equations

报告语言：中文&英文

报告时间：2023.05.10 09:00-10:00    
地点：MCM410
摘要: Compared to the soliton solutions, the breathers, which are constructed in the mKdV or Gardner equation via integrability methods, are less studied. In our numerical study, we show the interactions between two breathers, as well as between the breathers and solitons. We also find that breathers are as common as solitons, and thus, the breathers in the mKdV and Gardner equations can be considered as a special case. Numerical results also suggest the asymptotic stability for these breathers, which is only proved for the mKdV case, using the cubic nonlinearity. In general, we show that given a generic data, solutions will evolve into the combination of solitons and breathers, plus some radiation part. This phenomenon can be referred to as the "soliton-breather resolution conjecture". The talk is based on a joint work with Chandler Haight, Svetlana Roudenko and Diana Son. 

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报告人: Dr. Jacky Chong (北京大学)
题目: Derivation of the Vlasov equation from quantum many-body Fermionic systems with singular interaction

时间:2023.05.10 10:00-11:00
地点: MCM410
摘要: We consider the combined mean-field and semiclassical limit for a system of the N fermions interacting through singular potentials. We prove the uniformly in the Planck constant h propagation of quantum moments for the Hartree-Fock equation with singular pair interaction potential of the form |x-y|-a, including the Coulomb interaction. Using these estimates, we obtain quantitative bounds on the distance between solutions of the manybody Schrodinger equation and solutions of the Hartree-Fock and the Vlasov equations in Schatten norms. For a, we obtain global-in-time results when N. In particular, it leads to the derivation of the Vlasov equation with singular potentials. For a 2 ( 12 ; 1], our results hold only on a small time scale, or with an N-dependent cuto. The talk is based on our recent works in [1, 2, 3]. This is a joint work with Laurent Laeche and Chiara Saffrio. The talk will be delivered in English and is meant for the general audience.