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【學術報告】2016年1月19日下午我院将舉辦兩場學術講座

時間:2016-01-14

 

                 學術報告

(一)

報告人:C.D. Sogge

 

個人簡介:C.D.Sogge Johns Hopkins University 數學系 J. J. Sylvester 教授, 是國際上著名的國際調和分析與偏微分方程專家。在 Fourier 分析、偏微分方程等領域做出了許多傑出工作, 1994 年應邀在國際數學家大會上作 45 分鐘報告;已出版專著“Fourier Integrals in Classical Analysis”等,在重要的數學刊物上已發表學術論文 80 多篇,發表在 “Ann. of Math.”、 “J. Amer. Math. Soc”、“Acta Math.”、 “Invent. Math.” “ Duke Math. J.” 等國際頂尖數學期刊 20 餘篇。迄今為止已被引用 1200 多次,引用者包括 Fields 獎獲者 J. Bourgain, C. Fefferman, T. Tao 以及 Wolf 獎獲得者 E M Stein 等近 500 人; 現任重要數學期刊 “Amer. J. Math.”主編,也是“Forum Math.” 、“Disc. Cont. Dyn. Syst.”等學術期刊編委。 

 

題目improved eigenfunction estimates for the critical $L^p$-space on manifolds of nonpositive curvature"

 

摘要:I discuss recent improvements $L^{p_c}$-norms of eigenfunctions, where $p_c$ is the critical exponent $p_c=2(n+1)/(n-1)$ on manifolds of nonpositive curvature.  This estimate is sensitive to concentration at points as well as concentration along periodic geodesics.  It also yields improvements for all other exponents by interpolation or Sobolev estimates.  We are able to obtain this improved critical estimates using recent improved subcritical ones which are due to M. Blair and the author, as well as local harmonic analysis techniques and results of Bourgain and Bak and Seeger.

 

報告時間:2016年1月19日(星期二)下午14:30。

報告地點: 科技樓南樓702

 

(二)

報告人:Avraham Soffer 

 

個人簡介:Avraham Soffer 教授是 Rutgers 大學數學系傑出(Distinguished)教授,是 Alfred P. Sloan 獎獲得者、國際數學家大會 45 分鐘邀請報告人。他主要研究領域是數學物理和非線性偏微分方程,在量子多體散射、非線性孤立子(Soliton)穩定性研究中做出傑出貢獻,已完成論文 90 餘篇,其中在國際數學頂級雜志(如 Ann. Math, Invent. Math, CPAM,)發表論文多篇。

 

題目Nonlinear Long Range Scattering and Normal Form Analysis

 

摘要:First I will describe the source and nature of long range dynamics in

general. This fundamental effect is responsible to the change in the asymptotic
behavior of the system at large times. It is present in Coulomb and Gravitational dynamics, in theories with
mass-less particles (gauge theories) and in low power nonlinear
dispersive and hyperbolic equations.

Then, I will describe new results and new Normal Form techniques to deal
with the nonlinear Klein-Gordon equation in one dimension, with
quadratic and variable coefficient cubic nonlinearity. This problem
exhibits a striking resonant interaction between the spatial frequencies


of the nonlinear coefficients and the temporal oscillations of the
solutions. We prove global existence and (in L-infinity) scattering as
well as a certain kind of strong smoothness for the solution at
time-like infinity; it is based on several new classes of normal-form
transformations. The analysis also shows the limited smoothness of the
solution, in the presence of the resonances. In particular we observe
the phenomena of growth of some Invariant Sobolev norm of high order.
This seems to be generic for such nonlinear systems.

 

報告時間:2016年1月19号(星期二)下午16:00。

報告地點 :科技樓南樓702

 

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