学术报告

（一）

报告人：C.D. Sogge

个人简介：C.D.Sogge 是 Johns Hopkins University 数学系 J. J. Sylvester 教授, 是国际上著名的国际调和分析与偏微分方程专家。在 Fourier 分析、偏微分方程等领域做出了许多杰出工作, 1994 年应邀在国际数学家大会上作 45 分钟报告;已出版专著“Fourier Integrals in Classical Analysis”等,在重要的数学刊物上已发表学术论文 80 多篇,发表在 “Ann. of Math.”、 “J. Amer. Math. Soc”、“Acta Math.”、 “Invent. Math.” “ Duke Math. J.” 等国际顶尖数学期刊 20 余篇。迄今为止已被引用 1200 多次,引用者包括 Fields 奖获者 J. Bourgain, C. Fefferman, T. Tao 以及 Wolf 奖获得者 E M Stein 等近 500 人; 现任重要数学期刊 “Amer. J. Math.”主编,也是“Forum Math.” 、“Disc. Cont. Dyn. Syst.”等学术期刊编委。 

题目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.

报告时间：2016年1月19日（星期二）下午14:30。

报告地点： 科技楼南楼702

（二）

报告人：Avraham Soffer 

个人简介：Avraham Soffer 教授是 Rutgers 大学数学系杰出(Distinguished)教授,是 Alfred P. Sloan 奖获得者、国际数学家大会 45 分钟邀请报告人。他主要研究领域是数学物理和非线性偏微分方程,在量子多体散射、非线性孤立子(Soliton)稳定性研究中做出杰出贡献,已完成论文 90 余篇,其中在国际数学顶级杂志(如 Ann. Math, Invent. Math, CPAM,)发表论文多篇。

题目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.

报告时间：2016年1月19号（星期二）下午16:00。

报告地点 ：科技楼南楼702