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【2020.12.13-12.13 北京】Yang-Mills方程研討會
2020-12-13 | 編輯:

時間:20201213

地點:中國科學院數學與系統科學研究院南樓N202

組織者:張志濤,于萌   電話:13260231299

會議簡介:楊一米爾斯方程(Yang-Mills equation)是一個重要的微分方程,指楊一米爾斯作用量所確定的歐拉一拉格朗日方程,楊一米爾斯方程也叫做楊米爾斯理論。楊-米爾斯規范場存在性和質量間隔假設是七大千禧難題之一,為促進這一領域的發展,交流研究進展,我們組織這次Yang-Mills方程研討會。

 

日程安排:上午8:50-9:00, 開幕式,照相

學術報告

1.

時間: 上午9:00-10:00

報告人:陳建毅教授 (青島農業大學)

報告題目: 楊—米爾斯方程適定性問題的研究

摘要: 楊—米爾斯方程的建立是粒子物理發展的一個里程碑,該方程在微分方程理論、粒子物理標準模型的研究中發揮著重要作用。本報告介紹楊—米爾斯方程的物理來源與研究背景,以及在某些規范假設下楊—米爾斯方程解的適定性問題的研究進展。

2.

 時間:上午10:00-11:00

報告人:李奎教授(鄭州大學)

報告題目:The threshold theorem for energy critical hyperbolic Yang-Mills equation 摘要:In this talk, I will give an overview of the proof of Oh and Tataru’s Threshold Theorem for the energy critical hyperbolic Yang-Mills equation. It asserts that the (4+1) dimensional Yang-Mills system is globally well-posed in the caloric gauge for all topologically trivial initial data below twice the ground state energy.

3.

時間:上午11:00-12:00

報告人:羅海軍博士(湖南大學)

報告題目: The Yang–Mills heat flow and the caloric gauge

摘要In this talk, we are first concerned with the study of global solutions for the Yang–Mills heat flow, and establish sharp criteria for global existence and asymptotic convergence to a flat connection for this system.  Our second goal is to use the Yang–Mills heat flow in order to define the caloric gauge. And in this gauge, we can arrive at a good formulation of the hyperbolic Yang–Mills equation, which will play a major role in the proofs of the Threshold Theorem and the Dichotomy Theorem for  the hyperbolic Yang–Mills equation.

午餐、休息12:00-下午2:30

4.

時間:下午2:30-3:30

報告人:劉海東教授(嘉興學院)

題目:Existence and multiplicity results for a quasilinear Schrodinger equation

摘要:We consider the quasilinear Schrodinger equation

       

 where V is a potential function and N≥3. Under some natural assumptions on V and h, we prove some existence and multiplicity results. Our method relies on Jeanjean's monotonicity trick, decomposition of bounded Palais-Smale sequence, symmetric mountain pass theorem and Pohozaev identity. This talk is based on joint works with Dr. Yongtao Jing, Prof. Zhaoli Liu and Prof. Leiga Zhao.

5.

時間:下午3:30-4:30

報告人:孫冬冬教授(齊魯師范大學)

題目:Recent results on Schr?dinger-Kirchhoff equations

摘要:In this talk, we will give a list of results in recent years on Schr?dinger-Kirchhoff equations and we then show our recent results, which contain uniqueness and multiplicity results, results of equations with competing potentials and vanishing potentials, etc.

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